\ 


3 


IN  MEMORIAM 
FLORIAN  CAJORI 


A 
COMPENDIOUS 

SYSTEM 

O    F 


jratftcal 


AND 

DIVIDING  OF  LAND: 

CONCISELY     DEFINED, 
METHODICALLY     ARRANGED, 

AND 

FULLY    EXEMPLIFIED. 

THE  WHOLE 
ADAPTED  TOR  THE  EASY  AND  R  E  G  U  L  A  K, 

INSTRUCTION   OF    YOUTH, 

IN     OUR     AMERICAN     SCHOOLS. 


CO  M  PILED       BY 

ZACHARIAH    JESS, 

SCHOOLMASTER    IN    WILMINGTON. 

Copp  iRigtjt  gtcurefi  according  to  ILato. 

W  /  L  M  /  N  G  TON: 

PRINTED    BY    BONSAL    AND    NILES FOR    THE    COMPILER, 

—1799— 


PREFACE- 


AS  the  Treatifes  heretofore  publhlied  on  Surveying, 
are  deficient  in  examples,  whilft  they  treat  large 
ly  on  the  theory  ;  the  defign  of  this  publication  is,  to  fup- 
ply  fchools  with  a  fyftem,  exemplified  with  practical  illu  - 
ftrations,  fufEcient  to  give  the  learner  a  competent  know 
ledge  of  this  ufeful  fcience. 

To  avoid  fwelling  the  work,  and  increafing  the  price,  I 
have  omitted  giving  a  defcription  of  the  inftruments  ufed 
in  furveying  ;  as  they  are  better  underftoodby  infpe&ion, 
with  a  little  initru&ion  from  the  teacher,  than  by  any 
defcription  given  of  them. 

4 

I  have  chofen  a  fhort,  mechanical  method  of  explaining 

and  exhibiting  to  view,  the  dependencies  and  proportion 
al  properties  of  triangles,  in  order  to  meet  the  ideas  of 
the  learner,  in  the  moft  eafy  and  nmple  manner. — /This  I 
have  found  to  be  more  ufeful  to  them,  than  any  thing  I 
have  before  feen. 

I  have  not  enlarged  on  the  geometrical  method  of  de 
termining  the  Area  of  Maps,  as  it  is  not  to  be  depended 
«nj  for  although  it  may  appear  true,  upon  demonftrable 


IV 


PREFACE. 


principles,  I  have  found  by  experience,  that  as  many  dif 
ferent  ways  as  a  map  is  marked  into  triangles  and  trape 
ziums,  fo  many  different  areas  it  will  generally  gjve  ;  but 
I  have  inferted  a  fufiicient  number  of  examples  to  {how 
the  method,  which  may  anfwer  fome  purpofes  :  fuch,  as 
for  inftance,  a  man  to  determine,  nearly,  the  quantity  of 
land  in  his  own  fields  ;  arid  thefe  I  have  done  in  perches, 
and  tenths,  as  coining  neareft  to  the  truth  and  the 
larger  the  fc ale  the  better. 

The  calculations  by  difference  of  latitude  and  depar 
ture,  are  generally  made  in  chains  and  links,  as  being 
more  eafy  and  accurate,'  than'  in  perches, 'and  tenths — 
neverthelefs,  for  the  fake  of  fome  variety,  and  advantage 
of  thofe  who  prefer  the  latter,  I  have  given  fome  exam 
ples  calculated  in  perches,  and  tenths  j  and  it  will  evidently 
appear,  by  i'nfpe'&ion;  that  the  numbers  to  be  multiplied, 
tire  larger  j  and  as  it  is  cuftomary,  in^this  method,  to  re- 
]e&  the  fecond  decimal  figure,  it  cannot  be  fo  accurate— 
one  tenth  of  a  perch  fquare,  being  equal  to  6  J  fquare 
links.  '  H 

The  method  of  bringing  chains  into  perches,  is  very 
eafy  :  four  perches  being  one  chain;  therefore,  multiply 
the  chains  by  4,  and  the  product  will  be  perches,  and  the 
contrary.  ,  > 

EXAMPLES, 
I.  In  37.56  chains,  how  many  perches  ? 

37.56  x  4  =  150.^4  perches.     The  anfwer, 


PREFACE.  v. 

%.  In  150. 24  perches,  how  many  chains  ? 
150.34  -r-  4  as  37-56  chains.     The  anfwer- 
Note.  Thefe  two  examples  prove  each  other. 

Perhaps  fome  may  obje&  to  the  uniform  mode  I  have 
adopted,  in  finding  the  meridian  diftances.  I  know  that 
ibme  ufe  other  methods  ;  but  I  apprehend  there^is  none 
more  eafy,  than  the  one  I  have  chofen.  And  as  I  have 
found  by  experience,  that  a  variety  of  methods,  to  pro 
duce  the  fame  eflfeft,  contribute  more  to  confufe,  thin  in- 
ftru&  the  learner,  I  have  adhered  to  the  one  general 
mode. 

Should  this  work  merit  another  edition,  any  hint  for 
its  improvement,  will  be  gratefully  received,  and  duly 
attended  to,  by 

z,  y  E  s  s. 


IV 


PREFACE. 


principles,  I  have  found  by  experience,  that  as  many  dif 
ferent-ways  as  a  map  is  marked  into  triangles  and  trape 
ziums,  fo  many  different  areas'  it  will  generally  gjve  ;  but 
I  have  inferted  a  fufiicient  number  of  examples  to  fliow 
the  method,  which  may  anfwer  fome  purpofes  :  fuch,  as 
for  inftance,  a  man  to  determine,  nearly,  the  quantity  of 
land  in  his  own  fields  ;  arid  thefe  I  have  done  in  perches, 
and  tenths,  as  coming  neareft  to  the  truth— — and  the 
larger  the  fc ale  the  better., 

The  calculations  by  difference  of  latitude  and  depar 
ture,  are  generally  made  in  chains  and  links,  as  being 
more  eafy  and  accurate,  than  in  perches, 'and  tenths — ; 
neverthelefs,  for  the  fake  of  fome  variety,  and  advantage 
of  thofe  who  prefer  the  latter,  I  have  given  fome  exam 
ples  calculated  in  perches,  and  tenths  j  and  it  will  evidently 
appear,  by  i'nfpe'&ion;  that  the  numbers  to  be  multiplied, 
are  larger  ;  and  as  it  is  cuftomary,  in-this  method,  to  re- 
]e6l  the  fecond  decimal  figure,  it  cannot  be  fo  accurate— 
one  tenth  of  a  perch  fquare,  being 'equal  to  6  ~  fquare 
links.  '  •,  . 

The  method  of  bringing  chains  into  perches,  is  very 
eafy  :  four  perches  being  one  chain;  therefore,  multiply 
the  chains  by  4,  and  the  produft  will  be  perches,  and  the 
contrary 

EXAMPLES, 
I.  In  37.56  chains,  how  many  perches  ? 

37.56  x  4  =  150.54  perches.     The  anfwer. 


PREFACE.  v. 

2.  In  150. 24  perches,  bow  many  chains  ? 
150.34  -f-  4  =  37-56  chains.     The  anfwer* 
Note*  Thefe  two  examples  prove  each  othert 

Perhaps  fome  may  objeft  to  the  uniform  mode  I  have 
adopted,  in  finding  the  meridian  diftances.  I  know  that 
fome  life  other  methods  ;  but  I  apprehend  there  is  none 
inore  eafy,  than  the  one  I  have  chofen.  And  as  I  have 
found  by  experience,  that  a  variety  of  methods,  to  pro 
duce  the  fame  effeft,  contribute  more  to  confufe,  than  in- 
ftruft  the  learner,  I  have  adhered  to  the  one  general 
mode. 

Should  this  work  merit  another  edition,  any  hint  for 
its  improvement,  wiU  be  gratefully  received,  and  duly 
attended  to,  by 

z.  y  E  s  s. 


CONTENTS. 

SURVEYING,  Pagel 

Geometry,                                                 —  ibid. 

Geometrical  Definitions,         —                 _  3 

Pofitions,                  _ .                      _  jo 

Problems,                             —             —  l7 
Projeftion  of  the  Lines  Sines,  Tangents  and  Secants,    39 

Of  Guriter's  Scale,                              — -             —  43 

Of  Logarithms,              —                  —              — .  51 

Trigonometry,                     —                      —  63 

Right  Angled  Trigonometry,             —  65 

Oblique  Angled  Trigonometry,              —          —  80 

Heights,                                       _                  _  90 

Diftances,                                       — ,                  —  98 

To  find  the  Content  of  Land  Geometrically,  100 

To  make  a  Map  from  the  Field  Notes,           —  1 1 8 

To  find  the  Content  of  Land,  by  Calculation,  125 

Demonftration,  134 

To  make  a  Map  from  Difference  of  Lat.  and  Dep.  138 

Inacceffible  Boundary,  144 

Off-Sets,                                      —                 —  153 

Divifion  cf  Land,                  —  163 

To  make  a  Map  on  a  Circle,                              — *  177 

Interfe£tions,             —                                    —  188 

Atlraaion,                                                               —  200 

Variation,              —                —                     —  204 

To  enlarge  or  diminifli  Maps,                               —  206 

To  Survey  with  the  Chain  only,             —           —  208 


r  «&J"K{tf  5*2  •$£*&  *&*  *&  $£"*&  '^**T  ^fe^!!  «tjt*T  ts*r  *fc> 

53Bg8SBSS3B^9E3B3Byu3DgBgBaE®^9B 


SIGNS 

Ufed  in  this  Work. 


L 
•f 

X 


A 
S. 

Co-S. 
T. 

Co-T. 

Sec. 

Co-Sec 


>  Stand3 


"Degrees, 

Minutes, 

An  Angle, 

More;  or,  Addition) 

Multiplication, 

Equal  to, 

Divilion, 

Lefs;  Subtra£lion? 

A  Triangle,, 

Sine, 

Co-fine, 

Tangent, 

Co-Tangent, 

Secant, 

Co -Secant, 

Proportion ;  as  a  •  •  . 

Square-Root. 


THE 

PRINCIPLES 

O    7 

SURVEYING 


SURVEYING. 

SURVEYING   is  the  art  of  delineating  and  cal 
culating  the  content  of  land,  in  acres,  roods  and  per 
ches,  and  confifts  in  a  knowledge  of  geometrical  definiti 
ons  and  problems. 

GEOMETRY. 

GEOMETRY  is  the  fcience  wherein  we  confider  the  pro: 
perties  of  magnitude. 

G  E  O  M  E- 

B 


GEOMETRICAL    DEFINITIONS, 

USEFUL     fN     SURVEYING, 

I.  A  Point  is  the  fmalleft  fpace  that  can  be  affigned,  as 

£t  A  * 

a.  A  Line  is  the  neareft  diftance  between  two  points, 
£ind  15  confidered  without  breadth  or  thicknefs,  as  A  —  B. 

3.  Lines  equally  diftant  from  each  other,   -^  ^  __  jg 
In  all  their  parts,  are  called  parallel  lines,  as   V 
ABandCD.  J  C  -  D 

4.  The  inclination,  or    opening,  between  two  lines, 
which  interfeft  in  a  point,  is  .  called  an  Angle,  as  the  open 
ing  between  the  lines  AB  and  AC  ;  the  angle  is  gene 
rally  reprefented  by  three  letters,  thus  BAG,  the  mid- 
die  letter  being  at  the  .angular  point,  or  place  of  inter- 
fe&ion,  which  is  always  conlidered  to  be  the  centre  of 
p,  circle, 


B 


'C 


5.  When  one  line  {lands  on  another,  fo  as  to  incline 
neither  way,  it  is  a  perpendicular,  as  the  line  AC,  on  the 


GEOMETRICAL  DEFINITIONS.  3 

Uric  DE,  and  the  angles  on  each  fide  of  the  perpendicu 
lar,  are  right  angles. 


D 


A  Circle  is  any  diftance  taken  in  the  compares,  with 
otle  point  fixed,  and  the  other  carried  round,  and  the  line 
described  thereby,  is  called  the  circumference. 

7.  The  Diameter  of  a  circle  is  a  line  which  divides  ic 
into  two  equal  parts,  as  A  B. 

8.  The  Radius  of  a  circle  is  the  diftance  taken  in  the 
compaffes  to  defcribe  it,  and  is  half  the  diameter,  as  AC* 

9.  A  Semicircle  is  either  fegment  of  the  circle,  made 
fry  the  diameter,  as  AGB,  6r  AFB. 

ID.  A  Quadrant  is  half  a  femicircle,  and  is  contained 
between  half  the  diameter,  and  a  line  perpendicular  there 
to,  drawn  from  the  centre  of  the  circle,  as  CG.  r 


4  GEOMETRICAL  DEFINITIONS. 

ii.  A  Chord  of  a  circle  is  a  line  which  divides  the 
circle  into  two  unequal  parts,  as  DE,  and  it  is  a  chord 
to  both  fegments  of  the  circle,  as  DFE  and  DGE. 


12,.  A  Circle  is  actually,  or  fuppofed  to  be  divided  into 
360  equal  parts,  called  Degrees,  and  each  degree  into  60 
equal  parts,  called  Minutes;  and  thefe  into  feconds,  &c. 

13.  An  Angle  is  fo  many  degrees,  as  lines  drawn  from 
the  centre  of  a  circle,  include  thofe  parts  of  the  circle, 
thus  BAG  is  an  angle  of  30  degrees ;  becaufe  the  lines, 
AB  and  AC,  drawn  from  the  centre  of  the  circle,  include 
30  parts  of  360,  and  it  is  called  an  acute  angle,  becaufe 


GEOMETRICAL  DEFINITIONS.  3 

}t  is  lefs'  than  90  degrees,  and  BAD  contains  90  of  thofe 
parts,  and  is  therefore  an  angle  of  90°,  and  is  called  a 
right  angle,  becaufe  AD  is  perpendicular  to  AB,  and 
DAE  contains  no  of  thofe  parts,  and  is  an  angle  of  no 
degrees,  and  is  called  an  obtufe  angle,  becaufe  it  is  great 
er  than  a  right  angle  j  confequently  CAE  muft  be  130° 
and  an  obtufe  angle. 


V 


\ 


14.  A  Superfices  is  a  plain,  bounder!  tv  any  number  of 
Hnes ;  but  the  feweft  number  which  can  inclcfe  a  fuperfL 
ces,  are  three,  and  it  is  called  a  triangle,  as  ABC,  and  it 
is  a  right  angled  triangle,  becaufe  it  has  one  right  angle. 


GEOMETRICAL  DEFINITIONS. 


and  the  fide  AC  oppofite  the  right  angle,  is  called  thfc 
hypothenufe,  and  is  always  the  longed ;  the  other  two  are 
called  the  legs ;  the  upright  one  BC  the  perpendicular, 
and  the  other,  AB,  the  bafe. 


B 


15.  All  triangles  which  have  not  one  right  angle,  are 
called  oblique  angled  triangles,  whether  all  the  angles  be 
acute,  as  ABC,  or  one  angle  obtufe,  as  DEF, 


GEOMETRICAL  DEFINITIONS. 


1 6.  Any  figure  of  four  fides,  is  called  a  quadrilateral 
figure ;  and  if  the  oppofite  fides  be  parallel,  it  is  called  a 
parallelogram ;  and  if  all  the  fides  be  equal,  and  angles 
right,  it  is  called  a  fquare,  as  ABCD. 


17.  A  parallelogram,  whofe  oppofite  ftdes   are  equal, 
and  angles  right,  is  called  an  Oblong,  as  EFGH. 


GEOMETRICAL  DEFINITIONS. 


H 


1 8.  A  parallelogram  of  equal  fides,  and  angles  oblique, 
is  called  a  Rhombus,  as  ABCD,  and  it  is  equal  to  the 
right  angled  parallelogram  AJJLF- 

A  , ,B 


D  F  C  E 

<  19.  A  parallelogram  whofe  oppofite  fides  are  equal, 
and  angles  oblique,  is  called  a  Rhomboides,  as  GHIK, 
and  it  is  equal  to  the  right  angled  parallelogram  GHLM. 


M 


GEOMETRICAL  DEFINITIONS,  g 

ao.%  Any  quadrilateral  figure,  that  is  not  a  parallelo 
gram,  is  called  a  Trapezium,  as  ABCD,  and  is  equal  to 
the  two'  triangles  made  by  the  bafe  AC,  and  perpendicu 
lars  D  e  and  B  g. 


ai.  The  complement  of  an  angle,  is  what  it  wants  of 
5)0  degrees. 

22.  The  fupplenient  of  an  angle,  is  what  it  wants  df 
1 80  degrees. 

33.  The  angles,  in  every  triangle,  are   equal  to  tw<? 
tight  angles,  or  180  degrees. 


GEOMETRICAL 


G 


GEOMETRICAL  POSITIONS. 


*•  t  a  ^  H  E  angles  in  every  four  Tided  figure,  whether 
JL      it  be  right,  or  oblique  angled,  are  equal  to  four 
right  angles,  as  by  infpe&ing  the  preceding  figures  may 
plainly  appear. 

2.  Every  triangle  is  equal  to  half  aright  angled  paral 
lelogram,  made  on  the  bafe,  and  with  the  perpendicular 
height  of  the  triangle  j  thus,  the  triangle  ABC,  is  equal 
to  half  the  parallelogrom  ABCD  ;  and  the  line  AC,  is  a 
hypothenufe   to    the  two    equal  right  angled  triangles, 
ABC  and  ADC,  and  it  divides  the  two  right  angles,  viz. 
A  and  C,  each  into  two  angles ;  and  if  the  hypothenufe 
AC,  be  bife&ed  in  the  point  E,  then-  each  end,  viz.  AE 
and  CE,  will  be,  in  all  their  fimilar  parts,  equidiftant  from 
the  bafes  AB  and  CD,  and  from  the  perpendiculars  AD 
and  BC,  and  as  by  definition  4th.  the  angular  point  is  al 
ways  confidered  to  be  the  centre  of  a  circle ;  and  by  de 
finition  1 3th.  an  angle  is  fo  many  degrees  as  the  lines 
drawn  from  the  centre,  contain  parts  of  360,  the  degrees 
in  a  circle ;  therefore  the  angles  ACB  and   CAD,  are 
equal,  and  alfo  the  angles  CAB  and  ACD«are  equal;  it 
is  therefore  evidently  clear,  that  if  either  of  tbefe  angles 
be  fubtra&'ed  from  90  degrees,  the  remainder  will  be  the 
oppofite  angle,  both  on  the  fame,  and  oppofite  fides    of 
lllw  hypothenufe  ;  therefore,  in  every  right  angled  triaiv 


GEOMETRICAL    POSITIONS.       n 

gle,  i£  one  acute  angle  be  given,  fubtra£l  it  from  90  de^ 
grees,  the  remainder  will  be  the  other  acute  angle. 


3.  The  oblique  angled  triangle  DEF,  is  equal  to  half 
the  right  angled  parallelogram  DGFH,  and  each  angle  is 
the  fupplement  of  two  right  angles,  or  180  degrees  j  for 
a  fimicircle,  or  half  a  circle,  is  equal  to  180  degrees,  and 
it  is  evidently  clear,  by  infpe&ion,  that  if  the  inward  and 
outward  angles,  at  each  angular  point  of  the  triangle,  be 
added  together,  they  will  ma*:e  180  degrees;  therefore, 
in  every  oblique  angled  triangle,  the  fum  of  the  three 
angles  will  be  180  degrees  ;  and  if  either  angle  be  taken 
from  1 80  degrees,  the  remainder  will  be  the  fum  of  the 
other  two  angles ;  and  if  the  fum  of  either  of  the  two 
angles  be  taken  from  180,  the  remainder  will  be  the  other 
angle  :  all  which  will  evidently  appear  by  infpe£ling  the 
following  figure. 


GEOMETRICAL    POSITIONS. 

F 


Utiu*iu.iiu3k 

E  G 


4.  If  two  lines  crofs  each  other,  the  oppofite  angles 
will  be  equal,  and  the  two  angles  on  the  fame  fide,  will 
make  180  degrees,  which  is  equal  to  two  right  angles. 


5.  All  the  angles  that  can  be  made  from  any  one  point, 
on  the  fame  fide  of  a  line,  are  equal  to  two  right  angles, 


GEOMETRICAL  POSITIONS.        13 

or  1 80  degrees  ;  and  thofe  on  both  fides  of  the  line,  from 
the  fame  point,  will  be  equal  to  four  right  angles,  or  360 
degrees. 


6.  In  every  triangle,  if  one  fide  be  continued  in  the 
lame  dire&ion,  the  outward  angle  will  be  as  much  above 
90  degrees,  as  the  adjoining  inward  angle  is  lefs  than  90 
degrees,  and  equal  to  both  the  other  inward  angles,  which 
will  more  clearly  appear,  by  infpe&ing  the  following  fi 
gure,  and  that  in  pofition  3d.  than  by  long  demonflrations. 


G>  TRICAL    POSITIC 


7.  In  t  right  angled  triangle,  if  the  bafe  and  perpendi 
cular  be  equal,  and  the  hypothenufe  be  bife&ed  at  right 
angles,  and  die  bifefting  line  continued,  it  will  divide  the 
right  angle  into  two  equal  angles,  each  45  degrees,  and 
the  acute  angles  at  A  and  C,  are  each  45  degrees,  and 
the  four  angles  make  180  degre 


GEOMETRICAL,   POSITIONS.        15 

8.  In  a  right  angled  triangle,  as  DEF,  if  the  perpen 
dicular  be  longer  than  the  bafe,  and  the  hypothenufe  be 
bife&ed  at  right  angles,  the  bife&ing  line  will  interfetl 
the  perpendicular,  fo  that  the  upper  end  (cut  off  by  this 
bife&ing  line)  will  exa&ly  reach  from  the  place  of  in- 
terfeelion,  as  at  G,  to  the  extreme  end  of  the  bafe,  as 
to  D ;  thus  the  lines  DG  and  FG,  are  equal  in  length, 
and  becaufe  the  bafe  DE,  and  perpendicular  FE,  are  un 
equal  in  length,  the  acute  angles  at  D  and  F  are  unequal, 
and  the  greateft  angle  will  always  be  oppofite  the  lougefc 
fide.  And  as  DG  and  FG  are  equal,  the  angles  GDF 
and  FDG  are  equal,  by  pofition  7th. 


16       GEOMETRICAL    POSITIONS. 

A 

9.  In  an  oblique  an 
gled  triangle,  as  ABC, 
if  all  the  fides  be  equal 
in  length,  the  angles 
will  be  equal  in  quan- 
t  ity ,  and  each  60  de 
grees,  making  in  the 
whole  1 80  degrees,  as 
in  the  oppofite  figure: 


jo.  If  the  fides  of  a  triangle  be  unequal  in  length,  as 
GHI,  the  angles  will  be  unequal  in  quantity,  and  the 
greateft  angle  will  be  oppofite  the  longeft  fide,  and  the 
leaft  angle  oppofite  the  fliorteft  fide,  as  in  the  following* 
%urej  the  three  angles  taken  together,  making  two  right? 
angles,  or  iSo  degrees. 

i 


H 


ii.  If  two  fides  of  a  triangle  be  equal  in  length,  as  the 
fides  DE  and  FE,  in  the  following  figure,  are  equal,  then' 
the  angles  oppofite  thefe  equal  fides,  will  be  equal,  viz.' 
the  angles  at  D  and  F,  are  equal  to  each  other. 

E 


GEOMETRICAL  PROBLEMS* 


T 


PROBLEM    L 

O  draw  a  line  parallel  to  a  given  line  AB,  at  any 
diftance,  as  at  C. 

RULE. 


Take,  with  a  pair  of  compaffes,  the  neareft  diftance 
between  the  point  C,  and  the  line  AB,  and  with  that  di 
ftance,  and  one  foot  of  the  compaffes  in  the  line  AB,  as 
as  at  A,  defcribe  an  arch,  as  at  D  ;  then  from  the  point 
t,  draw  a  line  to  touch  the  arch  at  D,  and  it  is  done. 

G  D 


\ 


B  A 

PROBLEM    IL 

To  bife&,  or  divide  a  line  into  two  equal  parts, 

R    U    L    E» 

With  any  diftance  in  the  compaffes,  greater  than  half 
e  given  line  AB,  and  one  foot  of  the  compaffes  in  A't 

D 


i8        GEOMETRICAL    PROBLEMS, 

defcribe  the  arch  CD  ;  with  the  fame  diftance,  and  one 
foot  in  B,  crofs  the  former  arch  in  C  and  D,  draw  the 
line  CD,  and  it  is  done. 


D 


PROBLEM   in. 

To  raife  a  perpendicular  on  a  given  line,  as  AB,  from 
the  point  E. 

RULE. 

With  any  convenient  diftance  in  the  eompafies,  and  one 
foot  in  E,  make  a  point  on  each  fide,  as  at  c  and  e  ;  their 
open  the  compaffes  wider,  and  with  one  foot  in  c,  defcribe 
an  arch,  as  at  F ;  then  with  the  fame  extent,  and  one  foot 
in  e,  interfeft  the  former  arch  at  F,  draw  EF,  and  it  is" 
done. 


GEOMETRICAL    PROBLEMS. 


\ 


B 


PROBLEM    IV. 

To  ere&  a  perpendicular,  on  the  end  of  a  given  line, 
as  AG. 

RULE. 

With  any  diftance,  as  from  A  to  C,  in  the  compaffes, 
and  one  foot  in  C,  defcribe  a  circle,  fo  as  to  touch  the 
end  of  the  given  line  in  A ;  from  where  that  cuts  the  gi 
ven  line,  and  through  the  centre  C,  draw  a  line  to  cut 
the  circle,  as  in  B  ;  from  B,  draw  the  line  AB,  which 
witl  be  the  perpendicular  required. 


"i»  v 

/f  X  c     \ 

\      \  i 

L    '*  ^ 


ZQ        GEOMETRICAL    PROBLEMS, 

Or,  With  any  convenient  diftance  in  the  compaffes 
and  one  foot  in  the  end  of  the  line,  defcribe  an  arch  as 
FB,  fet  off  the  fame  diftance  from  B  to  E,  with  one  foot 
in  E,  defcribe  an  arch  at  G,  and  with  the  fame  diftance' 
turn  one  foot  over  to  F,  and  defcribe  an  arch  to  cut  the 
former  in  C ;  from  C  to  A,  draw  a  line,  and  it  is  done. 


C 


If 


•\ 


B 


PROBLEM    V. 

From  a  point,  as  at  C,  to  let  fall  a  perpendicular  on  the 
line  AB. 

RULE. 

With  one  foot  in  C,  defcribe  an  arch  to  cut  the  given 
line  AB ;  with  one  foot  in  each  place  of  interfe&ion,  de 
fcribe  arches  at  D,  and  from  C  to  D,  draw  a  line,  and  it 
is  done  ^  for  C  e  is  perpendicular  to  AB,  as  was  required, 


QEJOMETRICAL    PROBLEMS 


I 


B 


PROBLEM     VI. 

From  a  given  point  C,  to  let  fall  a  perpendicular  on  the 
end  of  a  given  line  AB}  at  B. 

RULE. 


From  any  point  in  the  line,  as  at  F,  with  the  diflance 
FC,  defcribe  anarch  atE  ;  choofe  any  other  point  in  the 
line,  as  at  D,  and  with  the  diftance  DC,  interfeft  the 
former,  arch  in:J^ ',  join  CE,  and  it  is  done  as  required. 


GEOMETRICAL    PROBLEMS, 


G 


A 


B 


PROBLEM    VIL 

To  make  a  right  angle  at  B,  on  the  line  BA. 

RULE. 

£re&  the  perpendicular  BC,  and  it  is  done. 

Or,  On  the  point  B,  and  with  the  chord  of  60  degrees 
in  the  conrbaffes,  ^efcribe  an  arch,  on  which  fet  ofF  90 
degrees  from  the  line  BA  to  C  j  then  draw  BC,  and  it 
is  done. 


GEOMETRICAL    PROBLEMS,        23 
C 


"""•••«, 


\ 


PROBLEM    VIII. 

To  make  an  angle  equal  to  any  number  cf  degrees,  fup- 
pofe  42°  30 /. 

RULE. 

With  the  chord  of  60  degrees  in  the  compafles,  on 
A  defcribe  ah  Arch  from  the  line  AB,  and  from  that  line 
lay  42, °  30 '  on  the  arch  to  D  ;  then  through  the  point 
D,  draw  AC,  and  it  is  done. 


D 


24        GEOMETRICAL    PROBLEMS. 


To  meafure  an  angle,  take  the  chord  of  60°  in  the  com'- 
pafles,  and  with  one  foot  in  the  angular  point,  make  an  arch 
from  line  to  HBC  ;  then  take  the  arch  in  the  compaffes,  apply 
it  to  the  chord,  which  will  fliew  the  degrees  ;  thus  the  preced 
ing  angle  will  meafure  42°  30'. 


PROBLEM    IX. 

To  make  an  obtufe  angle,  equal  to  ioi°   ao/. 

R  u  L.E. 

With  the  chord  of  60  degrees  in  the  compaffes,  on  B 
defcribe  an  arch,  on  which  from  C,  fet  off  60  degrees  to 
G,  and  from  G,  42°  ao/  to  D  ;  draw  BD,  and  it  is  done* 


o 
V 


GEOMETRICAL  PROBLEMS.      25 

PROBLEM    X. 

The  angles  and  hypothenufe  given,  to  find  the  legs. 

E  X  A  M  P  L  E. 

The  hypothenufe  1 2,  i  perches,  the  angle  opposite  the 
bafe  54°  30^;  confequently  the  other  angle  35°  30^  by 
pofition  ad.  page  lOj  the  bafe  and  perpendicular  are  re 
quired. 

R  u   L   E. 

Draw  the  line  CB,  and  on  C,  by  Problem  8,  make  an 
angle  equal  to  35°  3O/,  draw  CA  ;  take  in  perches  in 
the  compafles,  from  a  fcale  of  equal  parts,  and  fet  it 
from  C  to  A ;  then  (by  Problem  5)  from  A  let  fall  the 
perpendicular  AB  ;  then  the  perpendicular  AB,  being 
taken  in  the  compafles,  and  meafured  on  the  fame  fcale, 
will  be  70.25  perches,  and  the  bafe  CB,  98.5  perchesj 
as  required. 


j«5        GEOMETRICAL    PROBLEMS. 
PROBLEM    XL 

The  angles,  and  one  leg  given,  to  find  the  hypothenufe^ 
and  the  other  leg. 

EXAMPLE. 

The  angle,  oppofite  the  perpendicular  33°  15';  the 
bate  274  perches,  to  find  the  hypothenufe,  and  perpen 
dicular. 

RULE. 

Draw  CB,  equal  to  2,74  perches,  from  a  fcale  of  equal 
parts  ;  upon  B,  eredl  a  perpendicular,  by  Problem  3  ;  and 
on  C,  make  an  angle  equal  to  33°  15'  by  Problem  8; 
draw  C  A,  and  where  it  interferes  the  perpendicular,  wilt 
be  its  length;  then  the  hypothenufe  CA,  meafured  on  the 
fame  fcale,  will  be  3217.6,  and  the  perpendicular  BC, 
179.6  perches. 


GEOMETRICAL    PROBLEMS.        ay 
PROBLEM    XII. 

The  hypothenufe,  and  one  leg  given,  to  find  the  an- 
glesj  and  the  other  leg, 

EXAMPLE. 

The  perpendicular  69  chains,  hypothenufe  150  chains  j 
the  bafe  and  angles  are  required. 

RULE. 

Draw  the  bafe,  and  on  B  ere£l  a  perpendicular  to  A, 
equal  to  69,  from  a  fcale  of  equal  parts  ;  from  the  fame 
fcale,  take  150  in  the  cdmpaJGfes,  and  with  one  foot  in  A, 
let  the  other  fall  on  the  bafe,  as  at  C  ;  then  the  bale,  ta 
ken  in  the  compaffes,  and  applied  to  the  fame  fcale,  will- 
be  133,  and  the  angle  ACB,  meafured  on  the  chord  of  60 
degrees,  (by  the  note  to  Prombem  8)  will  be  27°  23'; 
confequently  the  other  angle  62°  37 /,  by  pofition  27 
page  JO. 


33        GEOMETRICAL   PROBLEMS. 

PROBLEM    XIII. 

The  legs  given,  to  find  the  angles  and  hypothenufe. 

EXAMPLE. 

The  perpendicular  980  perches,  the  bafe  690  perches; 
the  angles  and  hypothenufe  are  required. 

RULE. 

Draw  the  bafe  equal  to  690,  and  the  perpendicular 
equal  to  980  perches,  from  a  fcale  of  equal  parts  ;  then 
from  the  extremities  of  the  bafe  and  perpendicular,  draw 
the  hypothenuie  AC,  which  being  meafured  on  the 
fame  fcale,  will  be  1 198  perches,*  and  the  angle  at  C, 
meafured  on  a  chord  of  60°,  (by  note  to  Problem  8)  will 
be  54°  51'  -,  the  other  angle  35°  09',  by  pofition  ad. 


B 


GEOMETRICAL    PROBLEMS.         39 

*Note.  Two  fides  of  a  right  angled  triangle  being  given,  the 
third  may  be  feund  by  the  fquare  root  in  arithmetic,  or  extracted 
by  the  logarithms  as  hereafter. 

The  fum  of  the  fquares  of  the  bafe  and  perpendicular,  is  equal 
to  the  fquare  of  the  hypothenufe  ;  and  the  difference  between  the 
fquares  of  the  bafe  and  hypothenufe,  is  the  fquare  of  the  perpen 
dicular;  and  that  between  the  perpendicular  and  hypothenufe,  is 
the  fquare  of  the  bafe:  thus,  in  the  preceding  example,  the  fquare 
of  690,  the  bafe  is  476100;  and  the  fquare  of  980,  the  perpen 
dicular  is  960400  :  their  fum  is  1436500,  the  fquare  of  the  by- 
pothenufe,  the  fquare  root  of  which  is  1198,  the  length  of  the 
hypothenufe  in  the  fame  meafure  that  the  bale  and  perpendicular 
are. 

,  Again  :  If  from  1436500,  the  fquare  of  the  hypothenufe,  be 
taken  476100,  the  fquare  of  the  bale,  there  remains  960400,  the 
fquare  of  the  perpendicular,  its  fquare  root  is  980,  the  length  of 
the  perpendicular  ;  and  from  the  fquare  of  the  hypothenufe,  take 
the  fquare  of  the  perpendicular,  the  remainder  is  476100,  it* 
fquare  root  is  690,  the  length  of  the  bafe,  which  is  exemplified 
in  the  following  example,  where  the  bafe  is  6,  perpendicular  8^ 
and  hypothenuie  19. 


*o        GEOMETRICAL    PROBLEMS. 
PROBLEM    XIV. 

The  angles,  and  one  fide  of  an  oblique  angled  triangle 
given,  to  find  the  other  fides. 

EXAMPLE, 

The  angle  BBC  101°  25',  CBD  44°  42';  confequently 
the  other  angle  33°  50'  (by  pofition  3,  page  n)  and  the 
leg  BC  76  perches,  to  find  the  fides  CD  and  BD. 

RULE. 

Draw  BC  equal  to  76  perches  ;  on  B  make  an  angle 
equal  to  44°  42,',  and  on  C  an  angle  equal  to  33°  53': 
the  place  of  interfe&ion  will  determine  the  point  D  ;  then 
BD  being  meafured  on  the  fame  fcale,  will  be  43.2,  and 

54.5  perches,  as  required, 

I 

D 


76 

PROBLEM    XV. 

Two  fides,  and  an  angle  oppcfite  to  one  of  them  given, 
to  find  the  other  oppofite  angle,  and  third  fide. 


GEOMETRICAL    PROBLEMS.        31 

EXAMPLE. 

The  fide  BC  106  chains,  BD  65  chains,  and  the  angle 
at  C  31°  49',  to  find  the  angle  at  D,  and  fide  CD. 

RULE. 

Draw  the  line  BC,  equal  to  106  chains,  from  a  icale 
of  equal  parts  ;  make  an  angle  on  Cy  equal  to  31°  49'; 
take  65  chains  in  the  compafles,  and  with  one  foot  in  B, 
lay  the  other  on  the  line  CD  in  D  ;  then  the  angle  B,  be 
ing  meafured  on  the  chord  of  60  degrees,  will  be  2,7°  28', 
consequently  the  other  angle  120°  43'  (bypofition  3,  page 
1 1)  and  the  fide  DC  56.9  chains,  on  the  fc ale  of  equal 
parts. 


PROBLEM    XVI. 

•< 

Two  fides,  and  their  contained  angle  given,  to  find  the 
ether  angles,  and  third  fide. 

EXAMPLE* 

The  fide  BC   109,  BD  76,  and  angle  CBD  101°  30* 
,  to  find  the  other  angles,  and  fide  CD. 


GEOMETRICAL    PROBLEMS. 


RULE. 

Draw  the  line  CB,  equal  to  109  chains  or  perches  ;  BB 
^6,  from  a  fcale  of  equal  parts,  making  an  angle  on  B, 
equal  to  101°  30' j' join  DC,  and  apply  it  to  the  fame 
fcale  of  equal  parts,  and  it  will  be  144. 8,  and  the  angle  at 
I),  meafured  on  a  chord  of  60  degrees,  will  be  47°  3^', 
and  the  angle  on  C,  30°  58',  as  required. 


D 


109 


PROBLEM    XVII. 

The  three  fides  given,  to  find  the  angles. 

EXAMPLE. 

The  fides  EC  105,  BD  85,  and  CD  50  chains  or  per 
ches,  to  find  the  angles  at  B,  C  and  D, 


GEOMETRICAL   PROBLEMS.        33 


R  U  L  E> 

Draw  the  line  BC,  equal  to  105,  from  afcale  of  equal 
parts  ;  take  CD,  50  in  the  compafles,  and  with  one  foot 
on  C,  defcribe  an  arch  at  D  ;  then  take  BD,  85,  in  the 
compafles,  and  with  one  foot  on  B,  interfe&  the  arch  at 
D,  join  BD  and  CD  j  then  the  angle  at  B,  being  mea" 
fured  on  a  chord  of  60  degrees,  will  be  28 
C  53°  7';  confequently  the  angle  at  D, 
pofition  3. 


°  4',   and  at 
98°   49',  by 


B 


I05 


PROBLEM    XVIII. 

To  defcribe  a  circle  about  a  triangle  ABC,  or  through 
any  three  points  not  in  a  direct  line. 

RULE. 

Bife&  any  two  of  the  triangle's  fides,  at  right  angles, 
And  where  the  bife&ing  lines  interfeft,  is  the  centre  of 
the  circle,  as  atD,  the  diftance  from  which,  to  one  point 
of  the  triangle,  and  carried  round,  will  be  the  circle  rev 
Quired, 


GEOMETRICAL  PROBLEMS, 


PROBLEM     XIX. 

To  find  the  centre  of  a  circle. 

RULE. 

With  any  radius,  and  one  foot  in  the  circle,  as  at  Aj 
defcribe  an  arch,  as  CBD  ;  then  with  the  fame  radius, 
and  where  the  arch  cuts  the  circle,  defcribe  another  arch 
as  CAD,  and  through  the  points  of  interfe&ion,  draw 
the  line  CDG  ;  in  like  manner' draw  another  line  as  EFG, 
which- will  interfeft  the  other  line  in  the  centre  of  the 
circle  ;  for  each  of  thefe  lines,  if  continued,  will  be  a 
diameter  to  the  circle. 


GEOMETRICAL    PROBLEMS.        35 


C    .- 


PROBLEM    XX, 

To  make  a  right  angled  parallelogram,  whether  a  Iquare, 
$r  an  oblong. 

EXAMPLE, 

The  fides  AB  and  CD,  each  7  qhains  20  links ;  ths 
perpendiculars  AC  and  BD,  each  5  chains  40  links. 

RULE. 

Draw  AB  equal  to  7. 2  chains,  from  a  fc ale  of  equal 
parts ;  on  B  ere&  a  perpendicular  equal  to  5.4  chains  • 
then  with  AB  in  the  compaflfes,  and  one  foot  on  D,  de- 


36        GEOMETRICAL    PROBLEMS, 

fcribe  an  arch  at  C,  and  with  BD  in  the  compaffes,  with 
one  foot  on  A,  interfe&  the  former  arch  at  C  j  join  CA 
and  CD,  and  it  is  done. 


chains. 


D 


7.20  chains. 


B 


PROBLEM    XXI. 

To  make  a  Rhombus. 


EXAMPLE. 

Let  each  fide  of  the  Rhombus  be  6  chains,  35  links,  anct 
perpendicular  height  5  chains,  80  links. 

RULE. 

Draw  AB  and  CD  parallel,  at  the  diflance  of  5  chains, 
80  links;  then  take  6.35  chains  in  the  compafles,  lay  it 
from  C  to  D,  with  one  foot  in  D  ;  let  the  other  fall  in  the 
line  AB  at  B ;  turn  over  to  A,  join  the  feveral  corners 
by  lines,  as  in  the  figure,  and  it  is  done* 


GEOMETRICAL    PROBLEMS.        3.7 

, 
6.35  ch. 


6.35  chains. 

PROBLEM 

To  make  a  Rhomboides. 


xxn. 


EXAMPLE. 

Let  the  lines  AB  and  CD,  be  each  7  chains,  64  links  ; 
AC  and  BD,  each  5  chains,  35  links;  perpendicular 
height  4.85  chains. 

RULE. 

Draw  AB  and  CD,  parallel,  at  the  diftance  of  4.85" 
chains  ;  take  7.64  chains  in  the  compaffes,  andfet  it  from 
C  to  D  ;  take  5.25  chains  in  the  compares,  and  lay  it 
from  D  to  B  ;  make  BA  equal  to  CD  ;  join  the  feveral 
corners  by  lines,  as  in  the  figure,  and  it  is  done. 


7.64  chains. 


D 


7.64  chains, 


.gS        GEOMETRICAL    PROBLEMS. 
PROBLEM     XXIII. 

To  ma];e  a  Trapezium. 

EXAMPLE. 

Let  ABCD  be  the  boundary  lines ;  the  bafe  AC  64.4 
perches;  the  perpendicular  Bb  13.6,  and  Dd  37.3  per 
ches  ;  the  firft  perpendicular  from  A  18  perches,  the  2,d 
from  C  14  perches. 

RULE. 

Draw  AC  equal  to  64.4  perches  j  then  18  perches  from 
.4.,  raife  a  perpendicular  equal  to  13.6  perches  ;  and  14 
perches  from  C,  raife  a  perpendicular  equal  to  27.2  per 
ches,  on  the  oppofite  fide  of  the  bafe  AC  ;  join  the  feve- 
ral  boundary  lines,  as  in  the  figure,  and  it  is  done. 


3D 


GEOMETRICAL  PROBLEMS.       39 
PROBLEM      XXIV. 

To  divide  a  given  line,  as  AB,  into  any  number  of 
«qual  parts,  fupp'ofe  7. 

RULE. 

From  the  point  A,  draw  the  line  AC,  making  any  an 
gle  with  the  line  AB,  and  from  the  point  B,  draw  BD, 
parallel  to  AC  ;  then  with  any  convenient  oulance  in  the 
compafies,  on  the  lines  AC  and  BD,  and  from  the  angu 
lar  points,  turn  over  on  each  as  many  times,  lefs  enev 
than  the.  divifions  ;  join  the  fevcral  points,  and  the  line 
is  divided  as 


PROJECTION 


PROJECTION 

OF    THE    LINES    OF 

SINES,    TANGENTS,  AND  SECANTS* 

ON   THE    PLANE   SCALE* 


*.  TTT  I  T  H  any  convenient  radius,  defcribe  a  femi- 
*  *  circle  ADBC,  and  upon  the  centre  C,  raife 
trie  perpendicular  CD,  which  will  divide  the  femicircle 
into  two  quadrants  AD,  BD  ;  continue  CD  to  S ;  and 
upon  B  raife  the  perpendicular  BT ;  then  draw  the  lines 
BD  and  AD. 

2.  Divide  the  quadrant  BD,  into  9  equal  parts ;  then 
will  each  of  thefe  be   10  degrees,  which  may  be  fubdi-- 
vided  into  fingle  degrees  and  minutes,  if  the  radius  be 
large  enough  to  admit. 

3.  Set  one  foot  of  the  compaffes  in  B,  and  transfer  each 
of  the  divifions  in  the  quadrant  BD,  to  the  right  line  BD; 
then  is  BD  a  line  of  chords. 

4.  From  the  points   10,  20,  30,  &c.  in  the  quadrant 
BD,  draw  lines  parallel  to  CD,  till  they  cut  the  radius 
CB  j  then  is  the  line  CB,  divided  into  a  line  of  Sines. 


PROJECTION  OF  THE  LINE  OF  SINES,  &c.    41 

5.  From  the  centre  C,  through  the  feveral  divifions  of 
the  quadrant  BD,  draw  lines  till  they  cut  the  tangent  BT; 
fo  will  the  line  BT  become  a  line  of  tangents. 

6.  Set  one  foot  of  the  compafles  in  C,  extend  the  other 
to  the  feveral  divifions   10,  20,  30,  &c.  in  the  tangent 
line  BT,  and  transfer  thefe  extents,  feverally,  into  the 
line  CS  ;  then  will  the  line  CS  be  a  line  of  fecants. 

7.  Right  lines  drawn  from  A  to  the  feveral  divifions  10, 
30,  30,  &c.  in  the  quadrant  BD,  will  divide  the  radius 
CD  into  a  line  of  fines. 

8.  Divide  the  quadrant  AD,  into  9  equal  parts ;   and 
from  A  transfer  thefe  divifions,  feverally,  into   the  line 
AD  j  then  is  AD  a  line  of  chords. 


PROJECTION 


41   PROJECTION  OF  THE  LINE  OF  SINES,  &c. 


B 


O    F 

GUNTER's    SCALE. 


WHILE    the  reader  is  perufmg  the  following, 
it  will  be  proper  to  have  a  Gunter's  Scale  be 
fore  him. 

Gunter's  Scale  has  on  it  thefe  feveral  lines,  viz. 

I.  Sine  Rhumbs,  marked  S.  R.  is  aline  which  contains 
the  logarithms  of  the  natural  fine  of  every  point  and 
quarter  point  of  the  Mariner's  Compafs,  figured  from  the 
left  hand  toward  the  right,  with  i,  2,  3,  4,  5,  6,  7,  to 
8,  where  is  a  brafs  pin  ;  and,  where  it  can  be  done,  thefe 
are  divided  into  halves  and  quarters. 

3.  Tangent  Rhumbs,  marked  T.  R.  alfo  correfponds  to 
the  logarithm  of  the  tangent  to  every  degree  of  the  faid 
compafs,  and  is  figured  I,  3,  3,  4,  at  the  centre,  where 
there  is  a  pin;  and  from  thence,  toward  the  left  hand, 
with  5,  6,  7  :  it  is  alfo  divided,  where  it  can  be  done, 
into  halves  and  quarters. 

3.  The  Line  of  Numbers,  marked  Num.  contains  the 
logarithms  of  the  numbers,  and  is  figured  thus :  near 
the  left  hand  it  begins  at  I,  and  towards  the  right 
hand  is  a,  3,  4,  5,  6,  7,  8,  9  ;  and  then  i  is  the  mid- 


44          OF    G  U  N  T  E  R's     SCALE. 

die,  at  which  is  a  brafs  centre  pin,  going  ftill  on  2,  3,  4* 
5,  6,  7,  8,  9,  and  10  at  the  end,  where  there  is  another 
centre  pin;  the  firft  one  may  be  counted  for  i,  or  10, 
or  100,  or  1000;  and  then  the  next  2  is  accordingly  a? 
or  20,  or  200,  or  2000,  &c. 

Again ;  the  firft  I  may  be  reckoned  I  tenth,  or  I  hun 
dredth,  or  i  thoufandth  part,  &c.  then  the  next  2  is  2, 
tenths,  or  2  hundredths,  or  2  thoufandth  parts,  &c.  fo 
that  if  the  firft  i  be  efteemed  i,  the  middle  i  is  then  10, 
and  2  to  its  right  is  20 ;  3  is  30  ;  4  is  40  j  and  10  at  the 
end  is  100. 

Again ;  if  the  firft  one  be  10,  the  next  2  is  20;  3  is  30, 
and  fo  on,  making  the  middle  i  now  100 ;  the  next  2  is 
2OO;  3  is  300;  4  is  400,  &c.  and  10  at  the  end  is  now 
loco.  In  iike  manner,  if  the  firft  i  be  efteemed  i  tenth 
part,  the  next  2  is  2  tenth  parts ;  and  the  middle  i  is  i$ 
and  the  next  2  is  2,  and  10  at  the  end  is  now  10. 

Again  ;  if  the  firft  i  be  counted  i  hundredth  part,  the 
next  2  is  2  hundredth  parts  ;  the  middle  i  is  now  10  hun 
dredth  parts,  or  one  tenth  part  j  and  the  next  2  is  2  tenth 
parts  ;  and  10  at  the  end  is  now  but  one  whole  number, 
or  integer. 

As  the  figures  are  increafed  or  dimmifhed  in  their  va 
lue,  fo  in  like  manner  muft  all  the  intermediate  ftrokes  or 
fubdivifions  be  increaied  or  dimmifhed  >  that  is,  if  the  firft 
i  be  counted  i,  then  2  on  the  right  of  it  is  2,  and  each 
fubdivifion  between  them  now  is  one  tenth  part,  and 
fo  all  the  way  to  the  middle  i,  which  now  is  10,  the 


Qr    G  U  N  T  E  R's    S  C  A  L  E.          45 

next  2  is  20 ;  now  the  longer  ftrokes  between  one  ar4  % 
are  to  be  counted  thus,  n,  12,  where  is  a  brafs  pin; 
then  13,  14,  15  j  fometiraes  a  longer  ftroke  than  the  reft, 
1 6,  17,  1 8,  19,  20,  at  the  figures;  and  all  the  fliorter 
ftrokes  between  the  longer,  are  now  each  to  be  counted 
two  tenth  parts  from  the  mi4dle  i  to  the  next  2,  now  20 ; 
from  whence  the  longer  ftrokes  between  the  figures  are 
units,  thus,  21,  22,  23,  &c.  to  3,  which  now  is  30,  and 
thefhorter  ftrokes  each  between  them,  now  is  one  tenth 
part  of  an  integer ;  from  3,  each  fhort  ftroke  or  divifion, 
is  one  tenth  part  of  an  unit. 

Again ;  if  i  at  the  left  hand  be  10,  the  figures  between 
it  and  the  middle  I  are  common  tens;  and  the  fubdi- 
vifions  between  each  figure  are  units  ;  from  the  middle 
i  to  10  at  the  end,  each  figure  is  fo  many  hundredths  j 
and  between  thefe  figures,  each  longer  diviiion  is  10  > 
from  the  middle  i  to  2,  each  lefs  divilion  is  2  units ;  and 
from  2  to  the  end,  each  fliorter  divifion  is  5  units. 

From  this  defcription,  it  will  be  eafy  to  find  the  divifi- 
ons  representing  any  given  number,  thus  :  Suppofe  the 
point  reprefenting  1 2  is  required  ?  Take  the  divifion  at 
the  figure  i,  in  the  middle  for  the  firft  figure  of  12;  then 
for  the  fecond  figure,  count  2  tenths,  or  longer  ftrokes, 
to  the  right  hand,  and  this  laft  is  the  point  reprefenting 
1 2,  where  is  a  brafs  pin. 

Again  ;  fuppofe  the  number  22  is  required  ?  The  firft 
figure  being  2,  take  the  divifion  to  the  figure  2,  and  for 


46          OF     G  U  N  T  E  R?s     SCALE. 

the  fecond  figure  2,  count  2  tenths  onwards,  and  that  is 
the  point  reprefenting  aa. 

Again  ;  fuppofe  1728  is  required?  For  thefirft  figure 
i,  take  the  middle  i ;  for  the  fecond  figure  7,  count  on 
wards  as  before,  and  that  is  1700  ;  then  for'  the  third  fi 
gure  2,  count  2  tenths  from  the  laft,  and  it  reprefents 
1720;  laftly,  for  the  fourth  figure  8,  eftimate  8  parts  out 
of  10  of  the  next  fmaller  divifion,  this  point  reprefents 
1728. 

Required  the  point  reprefenting  the  number  435?  From 
4  in  the  fecond  interval,  count  towards  5  on  the  right 
hand,  three  of  the  large  divifions,  and  one  of  the  fmaller, 
and  that  will  be  the  divifion  expreffing  435,  and  the  like 
of  other  numbers. 

All  fra&ions  in  this  line  muft  be  decimals  ;  and  if  they 
be  not,  they  muft  be  reduced  into  decimals,  which  is  ea- 
fily  done  by  extending  the  compaffes  from  the  denomina 
tor  to  the  numerator ;  that  extent  will  reach  from  I  in 
the  middle,  to  the  decimal  required. 


EXAMPLE. 

Required  the  decimal  fra&ion  equal  to  -J-  ? 

Extend  from  4  to  3  ;  that  extent  will  reach  from  i  in 
the  middle  to  757  =  .75,  the  decimal  required,  towards 
the  left  hand ;  and  fo  of  any  other  vulgar  fraction. 


OF    GUNTER's    SCALE.         47 

MULTIPLICATION, 

Is  performed  on  this  line,  by  extending  from  I  to  the 
multiplier ;  that  extent  will  reach  from  the  multiplicand 
to  the  produ£l. 

Suppofe  it  is  required  to  multiply  16  by  4? 

Extend  from  i  to  4  j  that  extent  will  reach  from  16  to 
64,  the  produft. 

DIVISION, 

Being  the  reverfe  of  Multiplication  ;  therefore  extend 
from  the  divifor  to  i ;  that  extent  will  reach  from  the  di 
vidend  to  the  quotient. 

Required  to  divide  64  by  4  ? 

Extend  from  4  to  i ;  that  extent  will  reach  from  64  to 
16,  the  quotient* 

PROPORTION,  OR  THE  RULE  OF  THREE, 

Being  performed  by  Multiplication  and  Bivifion,  there 
fore  extend  from  the  firft  term  to  the  third;  that  .extent 
will  reach  from  the  fecond  to  the  fourth. 


EXAM  P  L  E. 

If  the  diameter  of  a  circle  be  7  inches,  and  the  circum 
ference  32, ;  what  is  the  circumference  of  another  circle, 
the  diameter  of  which  is  14  inches  ? 


43          Or    COUNTER'S    S  C  A  L  £ 

Extend  from  7  to  14  ;  that  extend  will  reach  .from  vk 
to  44,  the  circumference  required. 

In  like  manner,  may  any  other  proportion  be  worked. 
To  find  the  fuperficial  content  of  a  board,  plank,  &c. 

Extend  from  I  to  the  breadth  ;  that  extent  will  reach 
from  the  length  to  the  fuperficial  content. 

EXAMPLE. 

Suppofe  a  board  or  plank  15  inches  broad,  and  27  feet 
long ;  required  the  content  I 

Extend  from  I  to  I  foot  3  inches ;  that  extent  will 
reach  from  27  feet  to  33.75  feet,  the  fuperficial  content. 

Or,  Extend  from  12,  inches  to  15  inches,  &c. 

The  folid  content  is  found  by  extending  from  i  to  the 
breadth  ;  that  extent  will  reach  from  i  to  a  4th  number  . 
and  from  i  to  that  4th  number,  will  reach  from  the  length 
to  the  folid  content. 

EXAMPLE.     L 

What  is  the  content  of  a  fquare  pillar,  21  feet  9  inches 
long,  i  foot  3  inches  broad  on  each  fide  ? 

The  extent  from  i  to  1.25,  will  reach  from  1.25  to 
1.56,  the  content  of  i  foot  long.  Again  j  the  extent 


OF    G  U  N  T  E  R's    S  C  A  L  E.          4tf 

from  i  to  1.56,  will  reach  from  the  length  a  1.75 1033.98, 
or  34  feet  folid. 

EXAMPLE     II. 

Suppofe  a  piece  of  timber  1.25  feet  broad,  .56  foot  deep, 
and  36  feet  long ;  required  the  content. 

Extend  from'  I  to  1.35,  that  extent  will  reach  from. 56 
to  .7  ;  then  extend  from  i  to  .7,  that  extent  will  reach 
from  36  to  25.2  feet,  the  folid  content. 

The  line  of  Sines,  marked  Sin.  begins  at  the  left  hand, 
and  is  figured  thus :  i,  2,  3,  4,  5,  &c.  to  10 ;  then  20, 
30,  40,  &c.  to  90,  ending  at  the  right  hand,  where  is  a 
brafs  pin,  here,  and  in  all  lines  under  it :  thefe  figures  are 
called  Degrees. 

The  line  of  verfed  fines,  marked  V.  S.  begins  at  the 
right  hand,  againft  90°  on  the  fines,  and  from  thence  fi 
gured  towards  the  left  hand  thus :  10,  20,  30,  40,  &c. 
ending  at  the  left  hand,  about  169°  ;  each  of  the  fubdi- 
vifions,  from  10  to  30,  are  2  degrees,  and  from  thence  to 
90,  it  is  fingle  degrees  j  and  from  thence  to  the  end,  each 
degree  is  divided  into  15  minutes. 

The  line  of  Tangents,  marked  Tan.  begins  at  the  left 
hand,  and  figured  to  the  right,  thus  :  I,  2,  3,  &c.  to  10, 
and  fo  on  to  20,  30,  40  and  45,  where  is  a  brafs  pin,  juft 


5*          OF     G  U  N  T  E  R'  s     SCALE. 

under  and  even  with  90,  in  the  line  of  ftnes  ;  from  thencft 
back,  it  is  figured  50,  60,  70,  80,  &c.  to  89,  ending  at 
the  left  hand.  Where  it  began,  at  one  degree,  the  fub- 
divifions  are  as  the  fines. 

The  line  of  Meridional  Parts,  marked  Mer.  begins  at 
the  right  hand,  and  numbered  10,  30,  30,  to  the  left 
hand,  where  it  ends  at  87  degrees.  This  line,  with  the 
Hne  of  equal  parts,  marked  E.  P.  under  it,  are  ufed  to 
gether,  and  only  in  Mercator's  failing.  The  upper  line 
contains  the  degrees  of  the  meridian,  or  latitude,  in  Mer 
cator's  chart ;  and  the  lower,  the  equator,  and  contains 
^he  degrees  of  longitude* 


OF  LOGARITHMS. 


O     F 

LOGARITHMS 


LOGARITHMS   are  a  feries  of  numbers,  by 
which  the  work  of  multiplication  may  be  performed 
by  addition,  and  divifion  may  be  done  by  fubtra&ion ;  for, 
if  the  logarithm  of  any  two  numbers  be  added  together, 
the  fum  will  be  the  logarithm  of  the  produ&  :  and  if  the 
logarithm  of  the  divifor  be  fubtra&ed  from  the  logarithm 
of  the  dividend,  the  remainder  will  be  the  logarithm  of 
the  quotient :  and  if  the  logarithm  of  any  number  be  di 
vided  by   2,  the  quotient  will  be  the  logarithm  of  the 
fquare  root  of  that  number.     And  if  the  logarithm  of  any 
number  be  divided  by  3,  the  quotient  will  be  the  loga 
rithm  of  the  cube-root  of  that  number. 

To  find  the  logarithm  of  any  number  lefs  than  5  figures. 

EXAMPLES. 
To  find  the  logarithm  of  7. 

Look  in  the  table  for  the  number  7,  in  the  fide  co 
lumn,  and:  againft  it  is  .84510:  this  number  being  but 
one  figure,  the  index  to  the  logarithm  is  o. 


OF    LOGARITHMS. 

To  find  the  logarithm  of  79. 

Look  in  the  table  for  the  number  79,  in  the  fide  column, 
and  againft  it  is  .89763  ;  I  being  the  index,  becaufe  the 
given  number  has  two  figures. 

To  find  the  logarithm  of  763. 

Look  for  763  as  before,  againft  which  is  .88^52,  the 
jndex  being  2,  becaufe  the  given  number  has  three  figures. 

To  find  the  logarithm  of  7634, 

Find  the  three  firft  figures,  viz.  763,  in  the  fide  column 
as  before,  and  the  fourth  figure  4,  at  the  top  of  the  page ; 
thenoppofite  763,  and  under  4,  is  .88275,  to  which  pre 
fix  the  index  3,  becaufe  the  given  number  has  four  figures. 

To  find  the  logarithm  of  five  figures,  or  more. 

Suppofe  76345. 

Find  the  logarithm  of  the  four  firft  figures,  as  before, 
which  will  be  88275  ;  ta^e  tne  difference  between  this  lo 
garithm,  and  the  next  greater,  which  is  6 ;  then  fay,  if 
jo  give  6,  what  will  the  remaining  figure,  viz.  5,  give  ? 
thus,  If  10  .  .  6  :  :  5  .  .  3,  the  fourth  number  is  3, 
•which,  added  to  the  former  logarithm  88275,  gives  88278, 
to  which  prefix  the  index  4,  becaufe  there  are  five  figures, 
and  it  gives  the  logarithm  of  76345,  viz.  4.88278. 

To  find  the  logarithm  of  763458. 

Find  the  logarithm  of  the  four  firft  figures,  as  before, 
viz.  88275, 


Or    LOGARITHMS. 


53 


Take  the  difference,  as  before  ;  then  fay,  if  100  gives 
6,  what  will  the  remaining  figures,  viz.  58  give  ?  An- 
iwer  3  ;  which,  added  to  88275,  makes  88278,  to  which 
prefix  the  index  5,  and  it  gives  the  logarithm  of  763458 
to  be  5.88278. 

Note.  The  index  figure  is  always  one  lefs  than  the  number  of 
figures  in  the  given  whole  number,  whether  a  decimal  be  an 
nexed  or  not. 

Tp  find  the  logarithm  of  763,458. 

Find  the  logarithm,  as  before,  the  fame  as  if  the  figures 
were  all  whole  numbers  ;  then,  becaufe  there  are  but 
three  figures  in  the  integers,  prefix  the  index  2,  and  it 
gives  2.88278;  for  the  logarithm  of  763.458,  the  fame 
as  in  the  preceding  example,  only  in  the  index. 

To  find  the  number  anfwering  to  any  logarithm  of  four 
places  of  figures. 

What  is  the  number  to  the  logarithm  3.77342  ? 

Look  in  the  column  under  o,  and  there  the  next  lefs  lo 
garithm  will  be  7705,  oppofite  to  593  in  the  fide  column, 
then  look  directly  acrofs  the  page,  and  the  exact  logarithm 
will  be  found  under  5  at  the  top,  which  annex  to  593, 
makes  5935,  the  number  required. 

Note.  When  the  exact  logarithm  is  not  found,  it  is  ufual  to  take 
the  next  lefs,  or  neareft,  which  is  exact  enough  in  common 
bufincfs. 


54  Or    LOGARITHM  S, 

To  find  the  number  anfwering  to  a  logarithm  of  5^  or 
more  places  of  figures. 

What  number  anfwers  to  the  logarithm  4.59632  ? 

Take  the  difference  between  the  next  lefs  logarithm,  and 
the  given  one ;  alfo  the  difference  between  the  next  lefs 
and  greater  logarithms  ;  then  fay,  as  the  difference  between 
the  next  lefs  and  greater  logarithm,  is  to  the  .difference  be 
tween  the  numbers  anfwering  thereto,  (with  a  cypher  an 
nexed  for  every  unit  the  index  figure  is  more  than  3)  fo 
is  the  difference  between  the  next  lefs  and  given  loga 
rithm,  to  the  corre&ion  fought,  which  added  to  the  num 
ber  anfwering  to  the  neM:  lefs  logarithm,  gives  the  num 
ber  required.  What  is  the  number  anfwering  to  the  fol 
lowing  logarithm  ? 

4.59632  given  log. 

4.5962,7  The  ncarefc  lefs  log.  is  59627  its  num.   =39470 
The  next  greater  do.  is  59638  =r  39480 


Difference.  n  10 


As   ii   .  .   10  ::   5  .  .  4ff,  which  call  4.6;  and  ad 
ded  to  39470,  makes  35474.6  the  number  fought, 

MULTIPLICATION  BY  LOGARITHMS. 
R    U    L     E. 

To  the  logarithm  of  the  multiplicand,  add  the  loga 
rithm  of  the  multiplier  j  the  fum  is  the  logarithm  of  the 
produdud. 


Or    L  O  G  A  R  I  T  H  M  S.- 
CASE      I. 

to  fnd  tbe  producl  of   two  whole  or  mixed  numbers. 

Multiply  76,  log.  =  1. 88081 

%  45,  •=  1-73^39 

Produft  4104  =  2.6132:0 

Multiply  76.4  log.  «=  1.88309 
By  5.4          =  0.73239- 

Product     41^.56         =  2.61548 


CASE      2. 

When  both  or  either  of  tbe  faflors  are  less  than  unity, 

RULE. 

When  the  figure  next  to  the  decimal  point  is  part  p£ 
an  unit,  the  index  is  9  ;  but  if  it  be  o,  the  index  rnuft  be 
8  ;  and  as  many  cyphers  as  are  annexed  to  the  point,  fo 
many  units  the  index  mud  be  lefs  than  9;  fo  that  the 
number  of  cyphers  annexed  to  the  decimal  point,  and  in- 
index  figure,  taken  together,  muftmake  9  ;  and  in  adding 
thefe  logarithms,  ten  muft  be  rejected,  if  the  index  figure-s 
amount  to  ten. 

Multiply  76.  log,   =  1.88081 
By  45-  =   1-73*39 

Produd  4104.  »   3.61330 


56  Or     L  O  G  A  R  I  T  H  M 

Multiply  3.72         log.  =  0.57054 
By  .00064  =  6.80618 


Product   .0023808          SB  7-37672 


Multiply       59.4  log.  =   1.77415 
By         .000031  =  5.49206 

Produft  .0018414  c=  7.26621 


DIVISION  BY  LOGARITHMS. 
RULE. 

From  the  logarithm  of  the  dividend,  take  the  logarithm 
of  the  divifor,  the  remainder  is  the  logarithm  of  the  quo 
tient. 

In  fractions,  obferve  the  fame  rule  as  given  in  multipli 
cation  ;  and  when  the  index  figure  of  the  divifor  is  greater 
than  that  of  the  dividend,  10  muft  be  borrowed,  as  it  was 
rejected  in  addition. 

Divide   4104  log.  =  3.61321 
By  54  =   1-73^39 

Quotient  76  log.    =  1.88082 


Divide  410.4  log.  =  2.6132? 
By  5.4  =  0.73239 

Quotient  76.0  = 


OF    LOGARITHMS.  57 

Divide  .008215  log.  =  791461 
By         ,031  =  8.49136 

Quotient      .265  ==    9.42325 


Divide  .0023808  log.  =  7.3767^ 
By  3.72  =  0.57054 


Quotient     .00064  log.  =a  6.80618 

Divide   59.4  log.    =   1.774*5 
By   .000031  «  5,49209 

Quot.     .0001915  =  6.28206 


Note.  In  the  indices  here,  I  borrowed  ro,  in  the  fame  manner 
as  it  was  rejedled  in  Addition.     (See  Multiplication.) 

To  EXTRACT  the  ROOTS  ly  LOGARITHMS. 

The  logarithm  of  the  given  number,  divided  by  2, 
quotes  the  logarithm  of  the  iquare-root  of  that  number, 
and  divided  by  3,  quotes  the  logarithm  of  the  cube-root 
of  that  number. 

EXAMPLES. 

What  is  the  fquare-root  of  324? 
Log.  of  324,  is  =  2)2.51054 

Root  is  18,  its  log.  is  =  1.25527 

i 


5&  O  r    L  O  G  A  R  I  T  H  M  S. 

What  is  the  cube-root  of  10648? 

10648  log.  =  3)4*02736 
Root  is  22,  log.  ==  1.34243 

To  fnd  the  Root  of  a  Decimal  Fraction. 

For  the  fquare-root,  add  10  to  the  index  before  it  is 
divided ;  and  for  the  cube-root,  add  20,  &c. 

What  is  the  fquare-root  of  .001849? 

.001849  *ts  *°S'  is  —  7.26694 
Add  10 


2)17.26694 
Root  .043,  its  log.  is  =  8.63347 


What  is  the  cube-root  of  .125? 


5,  its  log.  is  ==  9.09691 
Add  20 


3)29.09691 
Root  is  .5,  its  log.  =  9.69897 


To  fnd  the  Logarithm  of  tbc  Sines,  Tangents,  and  Se 
cants,  belonging  to  any  number  of  Degrees  and  Mi 
nutes* 

RULE, 


OF    LOGARITHMS.  59 

RULE. 

If  the  degrees  be  lefs  than  45,  feek  them  on  the  top  of 
the  page,  and  the  minutes  in  the  left  hand  column  marked 
M,  againfl  which,  in  the  column  fignifted  at  the  top  with 
the  propofed  name,  (land's  the  fine,  tangent,  or  fgcant 
required ;  but  when  the  degrees  given,  be  more  than  45, 
feek  them  at  the  bottom,  and  the  minutes  in  the  right 
hand  column,  marked  M,  againft  which,  and  over 
the  propofed  name,  ftands  the  fine,  tangent,  or  fee  ant 
required. 

Obferve,  that  the  degrees  at  the  top,  and  minutes  in 
the  left  hand  column,  added  to  the  degrees  at  the  bot 
tom,  and  minutes  in  the  right  hand  column,  always  make 
90°  ;  hence,  if  a  fine  be  looked  for,  the  co-fine  or  comple 
ment  will  be  found  in  the  adjoining  column*  Obferve  the 
fame  of  tangents  and  fee  ants, 

EXAMPLES. 
Required  the  logarithm  fine  of  28°  37'? 

Under  28°,  and  oppofite  37',  in  the  left  hand  column, 
as  above,  and  under  the  word  Sine^  ftands  9.68029,  the 
logarithm  of  the  line  of  28°  37',  as  required. 

Required  the  logarithm  tangent  of  67°  45'? 

Find  67°  at  the  bottom  of  the  page,  and  45'  in  the 
right  hand  column,  oppofite  to  which,  and  over  the  word. 
Tangent,  ftands  10.38816,  the  log.  required. 


£o  OF     L  O  G  A  R  I,  T  H  M  S. 

The  logarithm  of  any  number  of  degrees  above  90,  is 
found  by  fubtrafting  the  given  degrees  from  180°, 
taking  the  logarithm  of  the  remainder. 


To  ftnd  the  Degrees,  Minutes^  and  Seconds,  to  any  gi^ 
gen  Logarithm* 

Find  the  degrees  and  minutes  correfponding  to  the 
neareft  logarithm,  which  is  exaft  enough  for  common  bu- 
fmefs  ;  but  if  feconds  be  wanted,  they  are  thus  found : 
take  the  difference  between  the  given  log.  and  the  next 
lefs  ;  alfo  between  the  next  lefs  and  greater  ;  then  fay, 

As  the  difference  between  the  next  lefs  and  greater  log. 
Is  to  60"; 

So  is  the  difference  between  the  next  lefs  and  given  logo 
To  the  feconds  required. 

But  if  they  be  required  to  a  given  log.  co-fine^  then  fay, 

As  the  difference  between  the  next  lefs  and  greater  log. 

Is  to  60"; 

So  is  the  difference  between  the  given  and  next  greater 

*?g< 
To  the  feconds  required. 

EXAMPLES. 

Find  the  degrees,  minutes,  and  feconds,  correfponding 
to  the  logarithm  fine,  9.61405. 


OF    LOGARITHM  3.  6s 

Next  greater  log.  9.61411  Given  log.  9.61405 

JJextlefs  9.61382  Nextlefs  9.61382 

29     Difference.  23 


As  29  .  .  60"  :  :  23  .  .  48",  to  be  Annexed  to  the 
degrees  and  minutes  correfponding  to  the  next  lefs  log. 
gives  24°  1 6'  48",  as  required. 

Find  the  degrees,  minutes,  and  feconds,  correfponding 
to  the  logarithm  co-fine  9.43x97. 

Next  greater  log.  9.43323         Next  greater  log.  9.43323 
Next  lefs  9-43278         Given  9-43-97 


45         Difference.  26 


As  45  .  .  60"  :  :  26  .  .  34",  to  be  annexed  to  the 
degrees  and  minutes  correfponding  to  the  next  lefs  log. 
gives  74°  1 6'  34",  as  required, 

To  find  the  Logarithm  Sins  or  Co -Sine,  for  Degrees, 
Minutes,  and  Seconds. 

Find  the  logarithm  to  the  degreees  and  minutes  ;  take 
the  difference  between  this  and  the  next  greater,  if  a 
fine ;  but  jf  a  co-fine,  the  next  lefs  ;  then  fay, 

As  6o// 

Are  to  this  difference  ; 
So  are  the  given  feconds, 

To  the  correction,  to  be  added  to  the  firft  logarithm, 
if  a  fine  ;  but  fubtra&ed,  if  a  -cc-fine. 


62  O»    LOGARITHMS, 

EXAMPLES, 

Required  the  logarithm  fine  of  24°  i6;  48'' 

Next  greater  log.  is  9.61411 
The  log.  of  24°  1 6',    is  9.61382 

29 


As  60"  .  .  39  :  :  48"  .  .  23,  to  be  added  to  9.6138:^ 
gives  9.61405,  the  log.  of  24°  16'  48",  as  required. 

What  is  the  logarithm  co-fine  of  74°  16'  34"? 

The  log.  of  74°  16'  is  9.433^3 
Next  lefs,  is  9-43278 

45 


As  6c"  .  .  45  :  :  34".  .26,  to  be  taken  from  9.43323, 
leaves  9.43297,  the  log  co-fine  of  74°  i6'34",  as  required. 


TRIGONOMETRY, 


TRIGONOMETRY, 

PLAIN  Trigonometry,  is  the  art.  of  meafuring  plain 
triangles,  by  comparing  fides  and  angles  together 
by  known  anologies ;  whereby  three  things  being  given 
a  fourth  may  be  found,  on  condition  that  one  of  them 
be  a  fide :  to  do  which,  right  lines  are  applied  to  the 
arch  of  a  circle,  deicribed  on  the  angular  point,  viz.  • 

A  chord  is  a  line  that  divides  the  circle  into  two  une 
qual  parts,  and  is  a  chord  to  them  both,  as  DH  is  the 
chord  of  the  arches  DH  and  DAH. 

2.  The  fine  of  an  arch,  is  a  line  drawn  from  one  end, 
or  termination  of  the  arch,  perpendicular  to  the  radius, 
or  it  is  half  the  chord  of  twice  the  arch ,  fo  that.  RS  is 
the  fine  of  the  arch  AS,  and  SZ  the  co-fine :  thft  fine 
and  co-fine  making  a  quadrant,  or  90°. 

3.  A  verfed  fine,  is  that  part  of  the  diameter  contained 
between  the  fine,  anil  the  arch,  as  RA  and  RGDr  and 
is  the  verfed  fine  of  SHD,  or  DEP  its  equal. 

4.  A  tangent  of  an  arch,  is  a  line  drawn  perpendicular 
to  one  end  of  the  diameter,  juft  touching  the  arch,  as 
AT  is  the  tangent  of  the  arch  AS,  and  HG  the  co-tan 
gent:  the  tangent  and  co-tangent  making   a  quadrant, 
or  90°, 


64  TRIGONOMETRY. 

5.  A  fecant  of  an  arch,  is  a  line  drawn  from  the  cen 
tre  through  the  circumference,  until  it  cuts  the  tangent, 
as  CT  is  a  fecant  of  the  arch  SA,  and  GC  the  co-fecant, 
meeting  the  co-tangent : ,  the  fecant  and  co-fecant  alfo 
a  quadrant,  or  90°. 


RIGHT     ANGLED 

TRIGONOMETRY. 


TH  E  folution  of  the  feveral  cafes  in  Right  Angled 
Trigonometry,  depends  on  the  following  Pofition, 
which  ought  to  be  well  committed  to  memory,  and,  by 
comparing  it  with  the  annexed  figures,  clearly  underftood 
by  the  learner,  before  he  prooeeds. 

POSITION. 

In  every  right  angled  triangle, 

If  the  hypothenufe  be  made  the  radius  of  a  circle^ 
the  other  two  fides,  or  legs,  will  be,  each  the  fine  of  its 
oppofite  angle. 

If  either  leg,  including  the  right  angle,  be  made  the 
radius  of  a  circle,  the  other  leg  will  be  the  tangent  of  its 
oppofite  angle,  and  the  hypothenufe  the  fecant  of  the  fame 
angle. 

The  foregoing  Pofition,  accurately  compared  with  the 
following  figures,  will  be  more  ihftrudive,  than  lengthy 
demonflrations. 


66        RIGHT  ANGLED    TRIGONOMETRY. 


\ 


Tag.  [  G         B 


RIGHT  ANGLED  TRIGONOMETRY*.        67 


^»»** 


Radi 


ms. 


\ 


.  When  the  hypothenufe  is  made  radius,  then  the  bafe  is 
the  fine  of  the  oppsfite  angle  C  ;  and  the  perpendicular,  a  fine 
of  the  oppofite  angle  A. 

When  the  perpendicular  is  made  radius,  then  the  bafe  is  tangent 
of  the  oppofite  angle  C,  and  the  hypethenufe  a  fecant  of  the 
fame  angle. 

And  when  the  bafe  is  made  radius,  then  the  perpendicular  is  tan- 
gent  of  the  oppofite  angle  A,  and  the  hypothenufe  a  fecant  of 
the  fame  angle. 

When  the  angles,  and  one  fide  are  given,  to  find  either, 
or  both  the  other  fides  ;  then  either  fide  may  be  made  ra* 
dius  ;  and  each,  in  rotation,  to  prove  the  work. 


RULE. 

As  the  name  on  the  given  fide, 
Is  to  the  fame  fide ; 
So  is  the  name  on  the  fide  required, 
To  the  fame  fide. 


68        RIGHT  ANGLED  TRIGONOMETRY. 

When  two  fides  are  given,  to  find  the  angles  j  then  one 
of  the  given  iides  muft  be  made  radius. 


RULE. 

As  the  fide  made  radius, 
Is  to  radius  ; 

So  is  the  other  given  fide, 
To  the  name  upon  it. 

CASE      i. 

The  Angles  and  Hypotbenuse  given,  to  fnd  the  Legs* 

Given,  the  hypothenufe,  12,1  perches  ;  the  angle,  op- 
pofite  the  bafe,  54°  30' ;  consequently  the  other  angle, 
35°  30/>  ty  pofition  a,  page  10. 

For  the  conftru&ion,  fee  Problem  10,  in  Geometry. 

C 


RIGHT  ANGLED  TRIGONOMETRY.        69 

By  making  the  Ease  Radius^  it  will  bey 
To  find  the  perpendicular  BC. 

As  fecant  [  A  35°  30'  10.08931 
Is  to  the  hypothenufe  121  2.08278 
So  is  tangent  [  A  35-3°  9-^53-7 

11.93605 

,10.08931 

To  the  perpendicular  BC  70.26    1.84674 

To  find  the  bafe  AB. 

As  fecant  |_  A  35°  30'  10.08931 
Is  to  the  hypothenufe  121  2.08278 
So  is  radius  90°  10.00000 

12.08278 
10.08931 


To  the  bafe  AB  98.5  J-99347 

By  making  the  Perpendicular  Radius,  it  will  to, 
To  find  the  perpendicular  BC. 

As  fecant  [  C  54°  30'  10.23605 
Is  to  the  hypothenufe  121  2.08278 
So  is  radius  90°  10.00000 

12.08278 
10.23605 


To  the  perpendicular  BC  70. 26    1.84673 


70        RIGHT  ANGLED  TRIGONOMETRY. 
To  find  the  bafe  AB. 

As  fecant  [  C  54°  30'     10.23605 

Is  to  the  hypothenufe        121  2.08278 

So  Is  tangent  [  C  54-30          10.14673 


12.2,2051 
10.23605 

To  the  bale  AB          98.5  1-99346 


By  making  the  Hypotbenuse  Radius ',  it  wilt 
To  find  the  perpendicular  £C. 

As  radivij  90°  10.00000 

Is  to  the  hypothenufe          121        2.08278 
So  is  fine  [  A         35°  30'  9-763<>5 

11.84673 

IO.OOOOO 


To  perpendicular  BG       70,26       1.84673 


To  find  the  bafe  AB, 

As  radius  90°  10,00000 

Is  to  the  hypothenufe  121  2.08278 

So  is  fine  [  C  54°  30"  -9.91069 


11.99347 

IO.OOOOO 


To  the  lafe  AB  98.5 


EIGHT  ANGLED  TRIGONOMETRY.        71 
BY    GUNTER's    SCALE. 

All  proportions,  where  fecants  are  not  in  them,  may 
be  worked  by  Gunter's  fcale  ;  the  extent  from  the  firft  to 
the  third  term,  will  reach  from  the  fecond  to  the  fourth  -, 
thus  the  laft  radius. 

i.  Extend  from  radius  90°  to  54°  30',  on  the  line  of 
fines ;  that  extent  will  reach  from  the  hypothenufe  131, 
to  the  bafe  98.5,  en  the  line  of  numbers. 

3.  Extend  from  radius,  1035°  30",  on  the  line  of  fines ; 
that  extent  will  reach  from  the  hypothenufe  121,  to  the 
perpendicular  70.2,6,  on  the  line  of  numbers* 

C    AS    E     2  &  3. 

The  Angles,  and  'one  Leg  given,  to  find  tbc  HypoiLe* 
nuse,  and  other  Leg. 

The  angle  oppoli'te  the  perpendicular  33°  15',  and  the 
bafe  274  perches,  are  given,  to  find  the  hypothenufe  and 
perpendicular. 

For  the  conftru&ion,  fee  Problem  n,  in  Geometry* 


2,        RIGHT  ANGLED  TRIGONOMETRY; 
By  making  the  Base  Radius,  it  will  bc^ 

To  find  the  perpendicular  AB. 

As  radius         90°  10.00000 

Is  to  the  bafe      274  2.43775 

So  is  tangent  [  C  33°  15'  9.81666 

12.25441 

IO.OOOOO 


To  the  perpen.  AB  17*9.6      2.25441 


To  find  the  hypothenufe  AC* 

As  radius  90°  10.00000 

Is  to  the  bafe        274  2.43 '77 5 

So  is  fecant  [  C  33°  15'      10.07765 


12.51540 

IO.OOOOO 

To  the  hypothenufe  327.6         2-51540 

By  making  tie  Perpendicular  Radius,  it  mil  be, 
To  find  the  perpendicular  AB. 

As  tangent  [  A  56°  45'     10,18334 

Is  to  the  bale  BC         274  2.43775 

So  is  radius  90°  10.00000 

12.43775 
10,18334 

To  perpendicular  AB  179.6  2.25441 


RIGHT  ANGLED  TRIGONOMETRY.        73 

To  find  the  hypothenufe  AC. 

As  tangent  [  A  56°  4$'     10-18334 

Is  to  the  bale  BG  274  2.43775 

So  is  fecant  [  A  56.45          10.26099 


12.69874 
10.18334 

To  hypothenufe  AC  327.6  2.51540 


By  making  tie  Hypotbenuse  Radius^  it  mil 
To  find  the  perpendicular  AB. 

As  fine  [A  56°  45'     9.92135 

Is  to  the  bafe  BC         274   *       2.43775 
So  is  fire  {•  C  33"  15'      9-739o£ 


12.17676 

9.92235 

To  perpendicular  AB  179.6       2.25441 


To  find  the  hypothenufe  AC. 

As  fine  [  A  56°  45'     9.92235 

Is  to  the  bafe  BC          274         2.43775 
So  is  radius  90°          IO.OGOOO 


12.43775 


To  hypothenufe  AC  327.6        3.51  540 
L 


74        RIGHT  ANGLED  TRIGONOMETRY, 

i 

BY     G  U  N  T  E  R. 

Extend  from  56°  45',  to  33°  15',  on  the  line  of  fines; 
that  extent  will  reach  from  274,  the  bale,  to  179.6,  the 
perpendicular,  on  the  line  of  numbers.  Again ; 

Extend  from  56°  45',  to  radius  90°,  on  the  line  of 
fines  ;  that  extent  will  reach  from  274,  the  bafe,  to 
3^7.6,  the  hypothenufe,  on  the  line  of  numbers. 

CASE      4  &  5. 

The  Hypotbenuse,  and  one  Leg  given?  to  find  the  An 
gles,  and  other  Leg. 

Given  the  perpendicular,  69  chains  or  perches  j  the 
hypothenufe  1 50,  to  find  the  angles  and  bafe. 

For  the  conftru&ion,  fee  problem  12,  in  Geometry. 


KIGHT  ANGLED  TRIGONOMETRY.        75 

By  making  tbe>  bypotbenuse  Radius^  it 
To  find  angle  C, 

As  the  hypothenufe  150         2.17609 

Is  to  radius  90°  10.00000 

So  is  the  perpendicular         69        1.83885 

11.83885 
2.17609 


To  fine  [  C  27°  23'  9.66276 


To  find  the  bafe  BC. 

As  radius  90°  10.00000 

Is  to  the  hypothenufe  150     2.17609 

So  is  the  fine  [  A        62°  37'       9.94839 

1 2.  i 2448 

IO.OOOOO 


To  the  bafe  BC  133.2  2.12448 

By  making  the  Perpendicular  Radius ,  it  will  be, 
To  find  angle  A. 

As  the  perpendicular  69         1.83885 

Is  to  radius  90°  10.00000 

So  is  the  hypothenufe         I£O       2.17609 


12.17609 

1.83885 

To  fecant  [A  62,°  37'       10.33784 


RIGHT  ANGLED  TRIGONOMETRY, 

To  find  the  bafe  BC. 

As  radius  90°  10.00000 

Is  to  the  perpendicular         ($9       1.83885 
So  is  tangent  [_  A         62°  37'     10.28568 


12.12453 

IO.OOOOO 


To  the  bafe  BC  133.2  2.12453 


BY     GUNTER. 

Extend  from  150,  the  hypothenufe,  to  69,  the  perpen 
dicular,  on  the  line  of  numbers  j  that  extent  will  reach 
from  radius  90°,  to  27°  23',  angle  C,  on  the  line  of  fines* 

Extend  from  radius,  90°,  to  62°  37',  angle  A,  on  the 
line  of  fines;  that  extent  will  reach  from  150,  the  hypo- 
thenufe,  to  133.2,  the  bafe,  on  the  line  of  numbers. 


CASE     6  &  7. 

The  Legs  given,  to  find  tbe  Angles   and  Hypotbemisc* 


Given  the  perpendicular,  980  perches  ;  the  bafe  690^ 
to  find  the  angles  and  hypothenufe. 

For  the  conftru&ion,  fee  problem  13,  in  Geometry. 


RIGHT  ANGLED  TRIGONOMETRY. 

A 


By  making  lie  Base  Radius,  it  will  bc^ 


To  find  angle  C« 

As  the  bafe  690 

Is  to  radius  90° 


3.83885 

IO.OOOOO 


go  is  the  perpendicular        980     3.99123 


To  tangent  [G         54 


ci' 


12.99123 
3.83885 

10.15238 


&        RIGHT  ANGLED  TRIGONOMETRY. 

To  find  the  hypothenufe  AC, 

As  radius  90°  10.00000 

Is  to  the  bafe  690  2.83885 

So  is  fecant  [  C         54°  51'       10.33979 

13.07864 
10.00000 


To  the  hypothenufe        1198       3.07864 

By  making  the  Perpendicular  Radius^  it  mil 

To  find  angle  A. 

As  the  perpendicular          980        3.99123 
Is  to  radius  90°  10.00000 

So  is  the  bafe  690          3.83885 


12.83885 
2.99133 

To  tangent  [A  35°  9'         9.8476* 


To  find  the  hypothenufe  AC, 

As  radius  90°  10.00000 

Is  to  the  perpendicular         980     3.99123 
So  is  fecant  [  A        35°   9'         10.08743 

13.07866 
10,00000 


To  the  hypothenufe        1198         3.07866 


RIGHT  ANGLED  TRIGONOMETRY.        79 

BY     G     U     N     T     E     R. 

The  extent  from  690  to  980,  on  the  line  of  numbers, 
will  reach  from  radius  45°,  to  54°  51',  on  the  line  o£ 
tangents. 

The  extent  from  33°  9',  to  radius  90°,  en  the  line -of 
fines,  will  reach  from-  690,  the  bafe,  to  1190,  the  hypo- 
thenufe. 


The  work  to  the  preceding  cafes  being  all  fet  down  ; 
and  as  a  good  knowledge  of  Trigonometry  is  the  bales  o£ 
the  Mathematics,  an  example  in  each  cafe,  with  their 
anfwers,  is  annexed,  for  the  benefit  of  the  learner. 

1.  Given  the  hypothenufe,  2,50  perches  or  chains  ;  the 
angle  oppofite  the  bafe,  54°  30',  to  find  the  bafe  and  per 
pendicular. 

Anfer;  the  bafe  203.5;  perpendicular  145.2* 

2.  Given  the  angle  oppolite  the  perpendicular  33°  15% 
the  bafe  325,  to  find  the  hypothenufe  and  perpendicular. 

Anfwer;  the  hypothenufe  388.6;  perpendicular  213.1. 

3.  Given  the  perpendicular  91  ;  the  hypothenufe  170, 
to  find  the  angles  and  bafe. 

Anfwer;  the  angle  oppofite  the  perpendicular  32°  22'; 
confequently,  the  other  angle  57°  38',  (by  pofition  2, 
page  10)  and  the  bafe  143.6. 

4.  Given  the  bafe  787  ;  the  perpendicular  890,  to  find 
the  angles  and  hypothenufe. 

Anfwer;  the  angle  oppofite  the  bafe,  41°  29';  confe 
quently,  the  other  angle  (by  pofition  2,  pa^e  10)  48°  31^ 
and  the  hypothenufe  n88. 


OBLIQUE      ANGLED 

TRIGONOMETRY, 

POSITION. 

IN  all  plane  triangles,  the  fides  are  in  direft  propor 
tion  to  the  fines  of  their  oppofite  angles ;    and  the 
Contrary. 

When  the  angles,  and  one  fide  are  given,  to  find  the 
•ther  fides,  or  either  of  them. 

RULE      i. 

As  the  fine  of  the  angle  oppofite  the  given  fidey 
Is  to  the  given  fide ; 

So  is  the  fine  of  the  angle  oppofite  the  fide  required, 
To  the  fide  required. 

When  two  fides,  and  an  angle  oppofite  to  one  of  them, 
*re  given,  to  find  the  other  angles  and  fide, 

RULE      2. 

As  the  fide  oppofite  to  the  given  angle, 
Is  to  the   fine  of  the  given  angle  ; 
So  is  the  other  given  iide, 
To  the  fine  of  its  oppofite  angle. 

Then  find  the  fide  (if  required)  by  Rule  iv 


OBLIQUE  ANGLED  TRIGONOMETRY.      Sx 

CASE       i. 

Two  Angles,  and  one  Side  given,  to  fnd  the  other  two 
Sides. 

The  angle  BDC  101°  25',  and  CBD  44°  4*',  and  the 
fide  BC  76  perches  given,  to  find  the  fides  CD  and  BD ; 
confequently,  (by  pofition  3,  page  n)  the  other  angle  is 
33°  53'- 

For  the  Conftruftion,  fee  problem  14,  in  Geometry. 

D 


To  find  DC, 
As  fine  fupplement  of  angle  D       101°  25'       9-99*3* 


Is  to  the  fid«  BC 
So  is  fine     B 


To  the  fide  DC 


76 


44°  4V 


54*53 


1.88081 
9.84720 

11.72801 
9.99132 

1.73669 


M 


82      OBLIQUE  ANGLED  TRIGONOMETRY, 
To  find  BD. 


As  fupplement  of  fine  [  D  101°  25' 

Is  to  the  fide  BC  76 

So  is  fine  I  C  33°  53' 


To  the  fide  BD 


43- 


9.99133 

1.88081 
9.74625 

11.62706 
9.99132 


By     GUNTER. 

The  extent  from  the  fupplement  of  [  D  =  78°  35',  to 
B  44°  42, y,  on  the  line  of  fines,  will  reach  from  the  fide 
C  76,  to  the  fide  DC  54.53,  on  the  line  of  numbers. 

The  extent  from  78°  35;,  to  [  C  33°  53',  on  the  line 
of  fines,  will  reach  from  the  given  fide  76,  to  the  fide 
BD  43*23,  on  the  line  of  numbers. 

C    A     S    E     2  &?  3. 

Two  Sides,  and  an  Angle  opposite  one  of  them   given^ 
to  find  the  other  Angles,  and  third  Side. 

The  fide  BG  106,  and  BD  65,  and  the  angle  BCD 
31°  49'  given,  to  find  the  other  angles,  and  fide  CD. 

For  the  conflruftion,  fee  problem  15,  in  Geometry. 


OBLIQUE  ANGLED  TRIGONOMETRY.    "83 

JNote»  When  the  given  angle  is  obtufc,  the  required  angle  will 
be  acute  ;  but  when  the  given  angle  is  acute,  then  it  is  Tome- 
times  doubtful,  whether  the  required  angle  be  qbtufe,  or  acute, 
and  ought  to  be  determined  by  drawing  and  viewing  the  figure, 
before  further  procedure ; 

Of  by  this  general  Rule. 

Square  each  fide  ;  then,  if  the  fquare  of  the  fide  oppofite  the  re- 
cjuired  angle,  be  more  than  the  ium  of  tke  jquares  of  the  ©ther 
two  fides,  the  required  angle  is  obtufe ;  it  they  be  even,  the 
angle  is  right;  and  if  the  fquare   of  the  fide    oppolite  the  re 
quired  angle,  be  lefs  than  the  fum  of  the  i<juare^  of  the  other 
tw0  fides,  then  the  angle  is  acute — thus,  in  the  foregoing  %iire, 
'  the 'required  angle  D,  is  obtufe, 

To  find  angle. D, 

AS  the  fide  BD  65  1.81291 

Is  to  fine  angle  G         .31°  49'       9.7.3198 
So  is  the  fide  BC  106  2.02531 


11.74729 
1.81291 


TofineoffupplementfD  59°  *7;1 
-i8o°-i20°  43' I  D          } 


By  pofition  3,  page  u,  angle  B,  will  be  found  to  be 
27°  28^ 


84     OBLIQUE  ANGLED  TRIGONOMETRY, 

To  find  the  fide  DC. 

As  fine  angle  C  31°  49'       9.72198 

Is  to  the  fide  BD  65          1.8129! 

So  is  fine  angle  B         2,7°  28'      9.66392 

11.47683 
9.72198 

To  the  fide  DC  56.86         1.75485 

BY     G  U  N  T  E  R. 

The  extent  from  65  to  106,  on  the  line  of  numbers,  will 
reach  from  31°  49/,  to  59°  17',  on  the  line  of  fines. 

The  extent  from  31°  49',  to  27°  28',  on  the  line  of 
fines,  will  reach  from  65  to  56.86,  on  the  line  of  numbers. 

CASE     4  &?  5. 

Tw0  Sides,  and  their  contained  Angle  given^  to  fnd  the 
Other  Angles',  and  third  Side* 

The  fide  BC  109,  BD  76,  and  their  contained  angle 
CBD  10 1 °  30'  given,  to  find  the  other  angles,  and  fide 
CD. 

RULE, 

As  the  fum  of  the  fides, 

Is  to  the  tangent  of  half  the  fum  of  the  unknown  an 
gles  ; 

So  is  the  difference  of  the  fides, 

To  the  tangent  of  half  the  difference  of  the  unknown 
angles. 


OBLIQUE  ANGLED  TRIGONOMETRY.      85 

To  half  the  fum,  add  half  the  difference,  and  the  fum. 
will  be  the  greater  angle ;  and  from  half  the  fum,  take 
half  the  difference,  and  the  remainder  will  be  the  lefs  an 
gle. 

For  the  conftru&ion,  fee  problem  16,  in  Geonetry. 

D 


B 


Side  BC     109 
BD      76 


109 


109     From  1 80° 
7  6     Take  i  o  i  °  3  o ',  the  given  angle. 


Sum  185  Diff.  33     Rem.    78°  30',  the  fum  of  the 

unknown  angles ;  (by  pofition  3,  page  1 1)  the  half  of  which 
fum,  is  39°  i5/. 

To  find  the  difference  of  the  angles  D  and  C. 

As  the  fum  of  the  fides  B  C  and  BD  =  185  2.26717 
Is  to  the  tan.  of  |-  the  fum  of  the  [s  C&D=39°i5'  9.91224 
So  is  the  diff.  of  the  fides  BC  and  BD  =  33  1.51851 

11.43075 
2.26717 


To  the  tang,  of  £  the  diff.  of  the  [  s  C&D  8°  17'  9.16358 


§6     OBLIQUE  ANGLED  TRIGONOMETRY. 

To  half  the  fum  of  the  angles,  39°  15',  add  half  their 
difference,  8°  17';  the  fum  is  47°  33',  the  greater  angle- 
D,  becaufe  it  is  oppofite  the  longer  fide  (by'pofition  10, 
page  1 6)  and  from  half  the  fum,  take  half  the  difference  ; 
the  remainder  is  30°  58',  the  lefs  angle  CP 

Having  the  angles,  the  fide  is  found  by  Cafe  I. 
To  find  DC. 

As  fine  angle  D         47°  32'  9.86786 

Is  to  the  fide  BC  109  "    2.03743 

So  is  fupplement  of  fine  angle  B  101°  301'         9.99119 

12.0286:4 
9.86786 


To  the  fide  DC  144.8  2.16074 


BY     G  U  N  T  E  R. 

The  extent  from  185  to  33,  on  the  line  of  numbers, 

will  reach  from  39°  i5Vto  $°  I7/>  on  t^ie  ^ne  °^  tan* 
gents'. 

The  extent  from  47°  32',  to  78°   30',  on  the  line   of 
fines,  will  reach  from  109  to  144-8,  on  the  line  of  numbers, 

C     A     S    E     6. 

Ibe  Sides  given,  to  find  the  Angles. 

The  fide  BC   105,  BD  85,  and  CD  50,  given,  to  find 
the  angles  BDC,  BCD,  and  CBD. 


OBLIQUE  ANGLED  TRIGONOMETRY.      87 


RULE. 

Divide  the  triangle  into  two  right  angled  triangles,  by 
letting  fall  a  perpendicular  from  the  point  D,  which  will 
divide  the  bafe  BC,  into  two  bafes  of  unknown  lengths, 
viz.  BA,  and  CA.  Then  fay, 

As  the  fum  of  the  bafes  B A  and  CA, 
Is  to  the  difference  of  the  fides  BD  and  DC  ; 
So  is  the  fum  of  the  fides  BD  and  DC, 
To  the  difference  of  the  bafes  BA  and  CA. 

Then  to  half  the  fum  of  the  bafes  BA  and  CA,  add 
half  their  difference,  and  the  fum  will  be  the  greater  baft; 
BA  ;  and  from  half  the  fum,  take  half  the  difference,  and 
the  remainder  will  be  the  lefs  bafe  CA. 

For  the  conftru&ion,  fee  problem  17,  in  Geometry. 

D 


The  fides 


/BD  85 

1CD  50 

Sum       135 


5° 
Diff.       35 


88     OBLIQUE  ANGLED  TRIGONOMETRY 

To  find  the  difference  of  the  bafes. 

As  the  fuhi  of  the  bafe  BA  and  CA        105       2.03119 

ts  to  the  difference  of  the  fides  BD  &  CD  35         1.54407 

So  is  their  fum.  135  21.13033 

3.67440 


To  the  diff.  of  the  bafes  BA  and  CA  4)45  1-65321 

22.5 

To  half  the  fum,  52.5,  add  half  the  difference,  22.5, 
the  fum  is  75,  the  greater  bafe  B  A,  and  fubtrafted,  leaves 
30,  the  lefs  bafe  CA. 

By  rigbt  angled  Trigonometry^  to  find  the  dngles* 
To  find  [  B. 

As  the  bafe  BA         75  1.87506         \ 

Is  to  radius  90°         10.00000 

So  is  the  hypothenufe  BD     85     1.92942 

11.92949 
1.87506 


To  fecant  [  B  28°  5'          10.05443 

To  find  [  C. 

As  the  bafe  CA     •     30  1.4771 4 

Is  to  radius  90°  10.00000 

So  is  the  hypothenufe  CD     50     1.69897 

11.69897 


To  fecant  [  C         53"  8'  10,22185 


OBLIQUE  ANGLED  TRIGONOMETRY.      89 

By  po/ition  3,  page  n,  ang.  C  53°  8  -f  28°  5',  ang. 
B  =  81°  13'  —  180  =  ang.BDC  98°  47',  the  feveral 
angles  required. 

BY    GUNTER. 

The  extent  from  105  to  135,  will  reach  from  35^45, 
on  the  line  of  numbers. 

The  extent  from  85  to  75,  on  the  line  of  numbers,  will 
reach  from  radius  to  61°  55',  on  the  line  of  fines,  [  BDA. 

The  extent  from  50  to  30,  on  the  line  of  numbers,  will 
reach  from  radius  to  ang.  ADC  36°  59',  on  the  line  of 
fines. 

Annexed  to  benefit  tbe  Learner. 

1.  Given  the  angle  B  DC  100°,  and  the  angle  DCB  54°, 
the  l(5g  BD  2,2,0  perches,  to  find  the  other  two  legs. 

Anfwer;  BC  267.8,  DC  119.2* 

2.  Given  the  fide  BC  365,  and  the  fide  AB   640,  the 
angle  BAG  26°,  to  find  the  other  fide  and  angles. 

Anfwer ;  the  fide  AC  808.7,  an?,  at  C  50°  14',  B  103° 
46'. 

3.  Given  the  fideBC  no,  AC  80,  and  their  contained 
angle  102°  30',  to  find  the  other  angles  and  fide. 

Anfwer  ;  the  greater  angle  45°  58',  the  lefs  angle  31° 
32',  and  the  third  fide  149.3. 

4.  Given  the  fide  BA  88,  BC  54,  AC  108,  to  find  the 
angles. 

Anfwer  ;  the  leaft  angle  29°  49',  next  greater  54°  07', 
and  the  greateft  96°  04'. 

N 


O    F 

HEIGHTS 


Note.  The  feveral  figures  in  Heights  and   Diflances,  are  drawn 
by  the  principles  of  the  preceding  Geometrical  Problems. 

PROBLEM    I. 

Te  find  the  Heigbt  of  a  perpendicular  Qbjeft,  at  one 
Station,  on  a  Plane. 

A     STEEPLE. 

f  The  angle  of  altitude  53  degrees, 
Given  -j  Diftance  to  the  foot  of  the  objeft,  85  feet, 
(.Height  of  the  obferver's  eye,  5  feet. 

RULE. 

By  Cafe  I,  or  2,,  in  Right  Angled  Trigonometry,  find 
the  perpendicular  ;  to  which  add  5  feet,  the  height  of  the 
obferver's  eye,  and  it  makes  1 17.8  feet,  the  height  of  the 
fteeple  required. 


The  work  in  this,  and  the  following 
problems,  is  omitted,  to  exercife  the 
judgment  of  the  learner  in  the  preced 
ing  rules, 


A  -•*•»-. 


85  feet. 


O    F      H    E    I    G    H    T    S.  91 

PROBLEM     II. 

To  find  the  Height  of  a  perpendicular  ObjeEl,  on   the 
Top  of  a  mil,  from  the  HilFs  Foot. 

r  Angle  to  the  bottom  48°  30', 
Given  \  Angle  to  the  top  67°, 

(.Diftance  to  the  bottom,   136  feet, 

RULE. 

By  Cafe  I,  .Oblique  Trigonometry,  the  angles  and  one 
fide  being  given  ;  thus,  the  angle  to  the  top,  67°,  its  com, 
plement  is  23°,  the  angle  at  C ;  then  the  difference  be 
tween  the  two  altitudes,  is  18°  30';  and  of  courfe  the 
angle  ABC  138°  30',  by  pofition  3  ;  hence  the  height  of 
the  objeft  will  be  found  to  be  1 10.5  feet.  And  by  Right 
Angled  Trigonometry,  the  height  of  the  hill  may  be  found 

:o  be  101,8  feet,  and  depth  to  the  perpendicular  diftance 

»f  the  objed  90. 1 2,  feet. 


rACB  23°, 
Angles  \  CAB   18°  30 
(.ABC  130.30. 


PROBLEM 


From  tie  Top  of  a  Hill,  to  find  the  Hclgbt  of  a  per 
pendicular  Object,  at  the  Foot   thereof. 


O 


F       HEIGHTS. 


rAngle  to  the  foot  of  the  objed  55°   15', 
Given  \  Angle  to  the  top  31°   15 V 

t  Diftance  to  the  foot  of  the  objed  250  feet. 

JZote.  By  the  fame  Cafe,  as  the  laft  Problem,  the  height  of  the 
ebjea  will  be  found  to  be  119  feet;  the  horizontal  diftance, 
P.s-AE,  142.5  feet,  and  height  of  the  hill  205.4  feet;  from 
the  height  of  the  hill,  take  the  height  of  the  objeft,  leaves  86.4 
feet  that  the  hill  is  above  the  objeft. 


f  ABE  34°  45'» 
CAB  24°, 
BCA  121  15', 

LECA  58"  45'. 


The  adding  and  fubtra&ing  thefe  angles,  are   omitted, 
to  try  the  judgment  of  the  learner. 

PROBLEM    IV. 

To  take  lie  Height  of  an  inaccessible  ObjcEl^  on  a  Plane^ 
at  two  Stations. 

rAngle  at  the  neareft  ftation  to  the  top  55°, 
Given  <  Stationary  diftance  87  feet  backwards, 

(_  Angle  at  the  fartheft  ftation  to  the  top  37°. 

RULE. 

By  Cafe  i,  Oblique  Angled  Trigonometry,  find  the 
diftance  from  either  itation,  to  the  top  of  the  objedl ;  from 
the  neareft  is  169.4  feet ;  from  the  fartheft  is  230.6  feet ; 
then,  by  Right  Angled  Trigonometry,  the  height  of  the 
objed  will  be  found  to  be  138.8  feet. 


OF      HEIGHT    S.  93 


Angles  -^ 


f  ACD  53°, 
BCD  35*, 
AGB  18°, 

LABC  135°. 


PROBLEM    V. 

Let  BC  be  a  pole  100  feet  high,  and  broken  off  as  at  D, 
fo  that  the  part  broken  off,  viz.  DC,  will  reach  from  the 
top  of  the  flump  to  A,  on  a  plane  34  feet  from  the  bot 
tom  or  foot  of  the  pole.  Required  the  length  of  the  part 
broken  off? 

RULE. 

In  the  right  angled  triangle  ABC,  the  bafe  and  perpen 
dicular  are  given,  to  find  the  angles  ;  and  by  Cafe  6  and  7, 
Right  Angled  Trigonometry,  the  angle  ACB  will  be  found 
to  be  18°  47',  and  i8°47/— 90°  =71°  13' CAB;  then 
by  pofition  8,  page  15,  interfe&  BC,  in  the  broken  place 
at  D;  then,  by  pofition  n,  page  16,  AD  and  CD  being 
equal,  their  oppofite  angles  muft  be  equal ;  therefore, 

ACB  18°  47' CAB  71°  i3/  =  DAB  52°  26';  then, 

in  the  right  angled  triangle  ABD,  the  angles  and  bafe  are 
given  to  find  the  hypothenufe  AD  55.77  feet,  the  part 
required. 

(See  the  following  figure.) 


94  OF      HEIGHTS. 

C 


A 


D 


B 


PROBLEM     VI. 

Jo  take  tbe  Height   of  a   perpendicular  Objefl,  on    a 
illy  at  two  Stations,  from  a  Plane  beneath  it. 


rFartheft  ftation,  angle  to  the  bottom  21°, 
~.          j  angle  to  the.  top  35°, 

j  Stationary  diftance  104  feet  dire&ly  forwards, 
LNeareft  ftation,  angle  to  the  top  48°  30', 

RULE. 

By  Cafe  I,  Oblique  Angled  Trigonometry,  find  the  di- 
ftanoe  from  the  fartheft  ftation  to  the  top  of  the  objeft, 


OF      HEIGHTS.  95 

viz.  333.6  feet ;  then  by  the  fame,  the  height  of  the  ob- 
je&  will  be  found  to  be  86.45  fee£' 

Note.  The  addition  and  fubtradion  of  the  angles,  are   omittei, 
to  exercile  the  judgment  of  the  learner. 


Angles 


f  ACB  13°  30' 
BAG  35.00 
DAG  14.00 
DAE  21.00 
ADC  1 11.00 
ABC  131.30 


104 


PROBLEM     VIL 

To  fnd  the  Length  of  an  ObjeEl  'which  stands  obliquely 
on  a  Hill,  at  two  stations,  on  a  Plane  beneath  it. 

rNeareft  ftation,  angle  to  the  bottom  36°  30', 

angle  to  the  top  44°  30' 
Given  -^  Stationary  dJftance,   104  feet  backward, 

I  Fartheft  ftation,  angle  to  the  bottom  24°  30', 
angle  to  the  top  32°. 


RULE. 

By  Cafe  i,  Oblique  Angled  Trigonometry,  find  the 
diftance  from  either  ftation  to  the  top  and  bottom  of  the 
object,  as  from  the  neareft  to  the  top  254.7  feet,  and  to 
the  bottom  207.4  feet ;  then  by  Cafe  4  and  5,  "the  length 
of  the  obje£l  may  be  found  to  be  57.15  feet. 


^6  OF       HEIGHTS. 

TACB  12°  30',  to  find  BC  254.7  feet, 

Andes  J  ADB  J2°'  to  find  BD  2°7'4  feet, 

1  CBD  8°,  to  find  the  length  of  the  objeft  57.15 


I 


feet. 


104  feet.  B  E 

PROBLEM     VIII. 

To  find  how  high  a  Person  at  Philadelphia,  must  be 
raised  into  the  atmosphere,  and  how  far  the  Sight  must 
extend,  to  see  London  /  the  Distance  being  51  De 
grees,  on  the  Rotundity  of  the  Earth,  and  the  Dia 
meter  of  the  Earth  7964  Miles. 

RULE. 

From  right  to  left,  draw  a  line,  to  reprefent  the  earth's 
diameter,  on  which  defcribe  a  circle  with  the  chord  of 
60°  ;  from  the  centre,  raife  a  perpendicular,  and  where  it 
cuts  the  circle,  will  reprefent  Philadelphia,  as  at  A,  from 
which  lay  off  51  degrees,  to  reprefent  London,  as  at  B  ; 
from  the  centre,  draw  a  line  to  B,  and  on  the  point  B, 
raife  a  perpendicular  to  interfeft  the  former  at  V  ;  then, 
in  the  right  angled  triangle  CBV,  the  angle  VCB  51°, 
and  bafe  CB  3982  miles,  are  given,  to  find  the  hypothnufe 


•"' 


OF       HEIGHTS. 


97 


CV,  from  which,  take  the  earth's  femidiameter,  leaves 
AV  2345  miles,  the  height  required ;  and  VB,  4917  miles, 
is  the  diftance  the  fight  imift  extend,  to  fee  London. 


Note.  The  operations  the  fame  as  Cafe  r,  Right  Angled  Trigo 
nometry. 


Philadelphia.^ 


OF  DISTANCES, 


O 


O    F 


DISTANCES, 


PROBLEM    I. 

LE  T  A  and  B  be  two  houfes  on  one  fide  of  a  ri 
ver,  393  perches  afunder ;  and  a  tower  at  C,  on 
the  oppofite  fide  of  the  river,  which  makes  an  angle  at 
A,  with  the  line  AB  of  53°  20' ;  and  at  B,  with  the  line 
BA  of  66°  20'.  Required,  the  diftance  from  the  tower 
to  each  houfe  ? 


,      /To  A  308.8  perches 
*  (.To 6270.5 perches 


Rote.  This  is  performed  by 
Cafe  i ,  Oblique  Angled  Tri- 
gonometry. 

A 


393  perches. 


PROBLEM    II. 

Let  B  and  C  be  two  houfes,  and  an  obferver  at  A  353 
perci  es  from  B,  and  230  from  C,  finds  that  they  make  an 
angle  at  A  of  70°.  The  diftance  between  the  houfes  is 
required? 


OF      DISTANCES.  99 


Ans.  277  perches, 

Note.  This  is  performed  by  Cafe  4  and 
5,  Oblique  Angled  Trigonometry. 


PROBLEM     III. 

Let  D  and  C  be  two  trees  in  a  bog,  and  an  obferver  at 
AandB  113  perches  afunder,  finds,  that  when  at  A,  the 
tree  at  D  mate  an  angle  with  the  line  AB,  of  100°  ;  and 
that  at  C,  makes  an  angle  with  the  line  AB,  of  36°  30' » 
and  when  at  B,  the  tree  at  D  makes  an  angle  with  the 
line  BA  of  49°,  and  that  at  C  of  iai°.  Required  the 
diftance  thefe  trees  are  afunder  ? 

Anfwer  232.5  perches. 

Note.  By  Cafe  T,  Oblique  Angled  Trigonometry,  find  the  di- 
flance  from  either  ftation  to  each  tree,  as  from  B  to  D  216 
perches;  and  to  C  175.6  perches  j  then,  by  Cafe  4  and  5,  find 
their  diftance  apart. 

D  C 


B 


TO    FIND    THE 

CONTENT  OF   LAND, 

GEOMETRICALLY. 
PROBLEM    I. 

To  find  the  Content  of  a  square  Piece  of  Land. 
RULE. 

Multiply  the  bafe  into  the  perpendicular,  and  if  they 
be  in  chains,  divide  the  product  by  10,  for  acres ;  and 
multiply  the  remainder  by  4,  for  roods,  and  by  40  for 
perches ;  but  if  in  perches,  divide  by  40  and  by  4,  for 
acres,  roods  and  perches,,  as  in  the  fubfequent  example. 

EXAMPLE. 

Let  ABCD A  be  a  fquare  field,  and  each  fide  7  chains 
29  links.  Required  the  content,  and  to  lay  down  a  map 
by  a  fcale  of  10  perches  to  an  inch. 

Chains.  Perches. 

7.29  =  '  29.16 

7.29  =  29.16 


A.  5,3.1441  4)0)85,0.3056 

4)21   10  P. 


R.    1,25764 


40  A.  5     i     10.3056 


P..  10,30560 


TO  FIND  THE  CONTENT  OF  LAND.      101 
D  G 


A.  R.   P. 

Ans.   5     i     10.3056 

Both  ways  the  fame. 


PROBLEM    II. 

To  find  the  Side  of  a  Square,  when  the  Content  is  given* 
RULE. 

Reduce  the  given  content  into  perches,  and  take  the 
fquare  root  thereof  for  the  tide  required  in  perches,  which 
reduce  to  chains. 

EXAMPLE. 

Required  to  lay  out  a  fquare  piece  of  ground,  which 
(hall  contain  12  acres,  3  roods,  and  16  perches,  and  to 
lay  down  a  map'thereof  by  a  fcale  of  2,0  perches  to  an  inch. 

A.    R.   P. 

Given  area  12     3     16 
4 


51 
40 

2 Perches.     Chains. 

v/2056  =  45.34  =   11.33-1,  one  fide  required, 

(See  the  above  Figure.) 


loa     TO  FIND  THE  CONTENT  OF  LAND. 
PROBLEM     III. 

To  find  the  Content  of  an  Oblong  Piece  of  Ground. 
RULE. 

Multiply  the  length  by  the  breadth,  and  divide  as  in 
Problem  i. 

EXAMPLE. 

Let  ABCD  be  an  oblong  piece  of  ground  7.2,5  chains 
long,  and  4.37  chains  wide.  Required  the  area  thereof, 
and  to  lay  down  a  map  by  a  fcale  of  20  perches  to  an  inch. 


Chains. 
Length  7.25 
Breadth  4.37 


Perches. 
29.00 
I7-48 

4)0)50(6.9200 
4)12     26  P. 


3A.     oR.     26P. 


P.  26592000 


A.  R.     P. 

Anfwer  3     o     26.92  ;  both  ways  the  Tame, 


B 


TO  FIND  THE  CONTENT  OF  LAND.      103 

PROBLEM     IV. 

The  Content  of  an  Qblong  Piece  of  Ground,    and  one 
Side  given)  to  fnd  the  other  Side, 

RULE. 

Divide  the  content  in  perches,  by  the  given  fide  in  per 
ches  ;  the  quotient  will  be  the  fide  required  in  perches. 

EXAMPLE. 

Suppofe  a  ditch  7.25  chains  long,  by  the  fide  of  which 
it  is  required  to  lay  out  a  piece  of  ground  that  fhall  con 
tain  3A.  oR.  36.92?.  the  breadth  from  the  ditch  is  re 
quired  ? 

A.  R.     P. 
3     o     36.92 

4 

12 

40 
p p. 

Given  fide  =  29)506.92(17.48  «=  4-37  chains. 

Note.  The  two  laft:  Problems  prove  each  other. 
(See  the  laft  Figure.) 

PROBLEM    V. 

To  fnd  the  Content  of  a  Rhombus,  or  Rhomboid?!* 

RULE. 

Multiply  the  length  into  the  breadth,  smd  divide  as  in 
Problem  i. 


304     TO  FIND  THE  CONTENT  OF  LAND, 

EXAMPLE. 

Let  ABCD  be  a  piece  of  ground,  in  form  of  a  Rhom 
bus,  or  Rhomboides,  whofe  bafe  AB,  is  1 1  chains,  and 
perpendicular  height  10  chains.  Required  the  oontent  ? 


Ch. 

Bafe  ii 

Perpendicular    10 

Acres  nlo 


Per, 
44 
40 


4lo)  I76JO 
4)44 

Acres  n  Anfwer* 


A 

PROBLEM    VL 

To  find  the  Content  of  a  Triangular  Piece  of  Ground* 
RULE. 

Multiply  the  bafe,  by  half  the  perpendicular? 
Or,  half  the  bafe  by  the  perpendicular; 
Or,  take  half  of  the  product  of  the  bafe  and  perpendiU 
cular  j  then  divide  as  before. 


"TO  FIND  THE  CONTENT  OF  LAND,      105 

EXAMPLE. 

Let  DBG  be  a  triangular  piece  of  ground,  thebafeBC 
12.38  chains,  and  perpendicular  CD  6.78  chains.  Re 
quired  the  content  ? 


Ch, 

Bafe  12.38 
i?er.  3.39 

A.  411.9682 
4 

,78728 
40 

P.  31149120 


Ch. 

l  Bafe  6*19 
Perp.    6.78 

S3  41.9682 


Ch. 

Bafe     12.38 
Perp.     6.78 


41.9682  fqt*;,  chains; 


Anfwer  4  A.     oR.     31.4912?* 

If  the  bafe  and  perpendicular  be  taken  in  perches,  i 
ill  produce  the 


D 


C 


io6      TO  FIND  THE  CONTENT  OF  LAND. 
PROBLEM     VII. 

The    Content    of  a  Triangular  Piece  of  Ground^  and 
the  Bass  given,  to  find  the  Perpendicular. 

RULE. 

Divide  the  content  in  perches,  by  half  the  bafe  in  per 
ches  ;  the  quotient  will  be  the  perpendicular  in  perches. 

EXAMPLE. 

Let  BC  be  a  ditch  12.40  chains  long;  by  which  it  is 
required  to  lay  out  a  triangular  piece  of  ground,  that  ihall 
contain  4  A.  iR.  joP.  Required  the  perpendicular? 

A.  fc.    P. 

Area  4     i     10 
4 


40 
C.  P.  -  P.         C.L. 

|  bafe  6.20  ==  24.8)690(27.  82=6.95  -J  perpendicular. 

(See  the  laft  figure.) 

PROBLEM    VIII. 

. 

To  find  the  Content  of  a  Trapezium. 

.RULE. 

Multiply  the  fum  of  the  perpendiculars  into  the  bafe, 
and  take  half  the  product  for  the  fquare  meafure,  and  di 
vide  as  in  Problem  i, 


TO  FIND  THE  CONTENT  OF  LAND. 

EXAMPLE. 

Let  ABCD  be  a  field,  in  form  of  a  Trapezium ;  the 
bafe  AC  1 6.10  chains,  the  perpendicular  B  b  3.40  chains, 
and  D  d  6.§o  chains.  Required  the  area  ? 

Note.  Bb  3.25  chains  from  A;  and  Dd  5.75  chains  frqm  C. 


Ch.       Ch.       Ch. 
Perpens.  6.80+3.40=10.20 
16.10 


Per. 

40.8  their  fum. 
64.4 


)  164,2200  =-1)2627.52 
82.1100    =»    1313.76=8    o    33.76 


PROBLEM    IX. 

To  jind  the  Content  of  a  Field,  bounded  by  four  Sides, 
two  of  which  are  parallel,  but  unequaL 

RULE. 

Multiply  the  Turn  of  the  parallel  fides  into  their  perpen 
dicular  diftance  ;  take  half  the  produ6l,  and  divide  as  in 
Problem  i. 


toS      TO  FIND  THE  CONTENT  OF  LAND. 


EXAMPLE. 

Let  ABCD  be  a  field,  and  the  parallel  fides  AD  and. 
BC  refpe&ively  7.20,  arid  12.25  chains  j  and  their  pen 
pendicular  diftance  15.40  ehainso  Required  the  area? 

Ch. 
Perpendiculars  4     ^^° 


Sum  of  perpen.     19.45 
Perpen.  diflance.  15.40 


P. 

77.80 
61.60 


.149-765°    •= 
ABCD  is  equal  to  ABEF, 


r 

D 


A 


3R. 


E 


P  R  O  B  L  E  M    X. 

Sides  of  a  Triangle,  find  their  contained  Angle 
given,  to  find  the  Area. 


TO  FIND  THE  CONTENT  OF  LANQ.     ioj>: 
RULE. 

As  radius, 

Is  to  the  log.  of  the  two  fides  ; 

So  is  the  fine  of  the  contained  angle  (or  its  fupplement 

to  1 80°,  if  obtufe) 
To  the  log.  of  the  double  area. 

EXAMPLE. 

In  the  triangle  ABC,  the  lines  AB  and  AC  refpe&ive* 
ly,  are  16.  and  10.12  chains,  and  their  contained  angle 
'30  degrees.  Required  the  area, 

As  radius  90°  10.00000 

.     ~,       TAB         1 6          1.20412 
Is  to  the  fides 


So  is  fine  of  the  angle         30°      9.69897 

11.90827 
10.00000 

To  double  area         1)80.96  1.90827 


P:  7,680 

,Area  4A.     oR.     7?. 

(See  the  following  Figure.) 


no      TO  FIND  THE  CONTENT  OF  LAND, 

G 


B 


r.  The  area,  and  two  fides  of  an  oblique  angled  triangle  givena 

to  find  the  third  fide. Invert  the  preceding  Rule,  thus  : 

As  the  product  of  the  given  fides, 

Is  to  radius  ; 

So  is  the  double  area, 

To  the  fine  of  their  contained  angle. 

Then,  by  Cafe  4,  Oblique  Angled  Trigonometry,  find  the 
third  {ide. 

PROBLEM      XI. 

To  find  tbe  Area  of  a  Circle,  or  an  Ellipsis* 

RULE. 

-  Multiply  the  fquare  of  the  circle's  diameter ;  or  the 
product  of  the  longed  and  Ihorteft  diameters  of  the  Ellip- 
fis,  by  .7854,  for  the  area. 

Or,  fubtraft  0.10491  from  the  double  logarithm  of  the 
circle's  diameter,  or  from  th'£  Aim  of  the  logarithms  of 
thole  elliptic  diameters,  and  the  remainder  will  be  the 
logarithm  of  the  area. 


TO  FIND  THE  CONTENT  OF  LAND.       n* 

Note.  In  any  Circle,  the 

Diameter  multiplied  \ ,  -    f  produces  the  circum. 

Circumfer.  divided    j^  3'14  59 1  quotes  the  diameter. 


EXAMPLE    i. 

How  matiy  acres  are  there  in  a  circle  of  one  mile  di 
ameter. 

Ch. 
i  mile  =  80 

80 

6400 
.7854 

A.    R.  P. 

Sqr.  Ch.    5026.5600  =  502     2     24-96 

Ch. 

1  i-9°3 


Log.  of  diameter  80  j 


3.80618 
0.10491 


Log.  of  area  5026.5  3-701^7 

Area  5O2.A.     2.R-     24?-  as  before. 

(See  the  following  figure.) 


TO  FIND  THE  CONTENT  OF  LAND, 


EXAMPLE    2; 

Suppofe  a  circle  of  100  perches  diameter,  is  inclofed 
with  a  wall  j  and  near  the  middle  of  this  inclofure,  is 
an  elliptical  Mi  pond  10  perches  long,  and  5  wide.  Re* 
quired  the  length  of  the  wall,  coHtent  of  the  inclofure^ 
and  area  of  the  pond  £ 

Diameter     100 
Multiplied  by  3.14159 


The  circumfer.    314.15900  perches* 


Or  take  314.16,  as  in  the  former  example,  the  content 
of  the  circumference  =  49  A.     oR.     14?, 

Elliptic 


TO  FIND  THE  CONTENT'  OF  LAND, 
Elliptic  diameters     -I 


P. 

ID         i.ooooG 
5   .     0.60897 


1.69897 
0.10491 

P.  1.59406 

Area  of  the  pond  39.27 


PROBLEM     XII. 

The  Area  of  a  Circle  given,  to  find  the  Dlam- 

RULE. 

To  the  logarithm  of  the  area,  add  0.10491,  and  h:i?£ 
the  fum  will  be  the  logarithm  of  tile  diameter. 

Or,  divide  the  area  by  .7854,  and  the  iquare  root  o£ 
the  quotient  will  be  the  diameter. 


iu      TO  FIND    THE  CONTENT  OF  LAND. 

EXAMPLE. 

Required  the  radius  of  a  Circle,  to  inclofe  one  acre  of 
ground  ? 

A.        P. 

I  B=  160         au3O4i$ 
0.10491 


i)^3°9°3 

The  diameter  ^14.37  1.15451  Log* 

The  radius       7.135  Anfwer. 


PROBLEM  xm. 

To  lay  out  an  Oblong  Piece    of  Ground,   so    that    tit 
Length  shall  bear  a  given  Proportion  to  the  Breadtb* 


TO  FIND  THE  CONTENT  OF  LAND.       115 

RULE. 

As  the  lefs  number, 
Is  to  the  given  area  in  fquare  perches-; 
So  is  the  greater  number, 

To  the  fquare  of  the  longeft  fide  ;  (the  fquare  root  o£ 
which  will  be  the  longeft  fide  in  perches). 

AND, 

As  the  greater  number, 
Is  to  the  given  area,  in  fquare  perches  j 
So  is  the  lefs  number, 

To  the  fquare  of  the  fhorteft  fide  ;  (the  fquare  root  of 
which,  will  be  that  fide  in  perches.) 

EXAMPLE. 

Let  it  be  required  to  lay  out  an  oblong  piece  of  ground 
to  contain  864  acres,  and  the  breadth  to  bear  the  fame 
proportion  to  the  length,  as  3  does  to  5. 

864  acres  =  138240  perches. 

a 

As  3  .  .  138240  :  :  5  .  .  ^230400  «s  480  perches, 

the  length  required. 


$ 

the 
D 

A 

is  5  .  .   138240  :  ;  3  .  .  ^82944    am    288  percb 
breadth  required. 

es 
C 

B 

lie.      TO  FIND  THE  CONTENT  OF  LAND, 


PROBLEM    XIV. 

To  lay  out  an  Oblong  Piece  of  Ground^  so  that  tb? 
Length  shall  exceed  the  Breadth,  by  a  given  Differ 
ence* 

RULE, 

To  the  given  area,  add  (he  fquare  of  half  the  differ-' 
£nce  ;  and  to  the  fquare  root  of  their  fum,  add  half  the 
difference,  for  the  length  j  and  from  that  fquare  root,  take 
half  the  difference,  for  the  breadth, 

EXAMPLE, 

Required  to  lay  out  an  oblong  piece  of  ground,  to  con 
tain  47  A.  aRo  i6]p.  and  to  be  80  perches  longer  than 
wide. 

47A.  VR.  i6P.  ~  7616  perches. 
1600 

40  x  40  =  1600  -x/9216    ==  96 

Add  and  fubtra^b  half  diff.  4© 


D 


r        f  Length 
Anfw'    {Breadth     56 


TO  FIND  THE  CONTENT  OF  LAND.      117 
PROBLEM     XV. 

To  make  the  proper  Allowances  for  Roads,  ^c. 

In  laying  out  new  lands,  it  is  cuftomary  to  snow  6 
acres  to  every  100,  for  roads.  The  land,  with  this  al 
lowance,  may  be  called  Gross  ;  and  with  this  allowance, 
dedu&ed,  it  may  be  called  Neat. 

RULE. 

The  grofs,  divided    ~)  ,  6  f  quotes  the  neat  ; 

The  neat,  multiplied  J    y  \  produces  the  grots. 

EXAMPLES. 

1.  How  much  land  muft  be  inclofed,  to  have  850 A. 
2,R.'  2oP.  neat. 

40)20 

4)^-5 
..   ;J  •  Acres. 

850.625  x  i. 06  =901.6625  as  9QiA.  2R.  ^6P.  Anfw. 

2.  How  much  neat  meafure  is  there  in  a  tra.,61  of  901  A. 
aR.  2  6 P.  grofs  ? 

40)26 
4)   2.65 


1.06)901.6625(850.625  t=  85oA.  2R.  2oP.  Anfwer 


.  Thefe  two  examples  prove  each  other. 

Any  quantity  of  land  may  be  laid  out,  or  incloied,  in 
the  form  of 

p  Square  By  Problem  II.  "    Page   icr 

i  Oblong,   T  fide  given  IV. 

*     1  proportion  given,,  XIII. 

' 


|  dhT.  of  Ij2\&Bear.  given,  XIV. 

Triangle,  the  bale  given,  VII. 

I  Circle,  XII. 


103 
114 
116 
106 
115 


>i8      TO  FIND  THE  CONTENT  OF  LAND. 

P  R  O  B  L  E  M    XVI. 

To  Map  a  Survey,  frovi  the  Field  Notes%  and  find  tfo 
Content  thereof. 

RULE. 

Draw  a  line  on  the  paper,  to  reprefent  the  firft  meri 
dian  ;  put  N  at  the  top,  for  North  ;  S  at  the  bottom,  for 
South  ;  E  at  the  right  hand,  for  Eaft  ;  and  W  at  the  left 
hand,  for  Weft ;  (for,  in  making,  or  viewing  maps,  we 
always  fuppofe  to  face  the  North)  then,  in  a  convenient 
place,  make  a  point  in  the  line,  for  the  firft  ftation ;  lay 
the  ftrait  edge  of  the  Protra&or  to  the  line,  with  the  cen 
tre  mark  to  the  point ;  turn  the  arch  of  the  Protraftor  Eaft 
or  Weft,  as  the  bearing  is  j  and  from  the  North  or  South 
end  of  the  Protraftor,  as  indicated  by  the  bearing,  prick 
off  the  degrees  mentioned;  then,  through  this  point,  draw 
a  line  from  the  firft,  on  which  lay  the  firft  diftance,  and 
through  this  laft  point,  draw  a  line  parallel  to  the  firft  me 
ridian  :  to  this  fecond  meridian,  and  at  the  end  of  the 
firft  diftance,  lay  the  Protra&or  as  above  faid,  and  fo  pro 
ceed  from  ftation  to  ftation,  and  clofe  at  the  place  of  be 
ginning.  Then  difpofe  the  map  into  triangles  and  trape 
ziums  ;  meafure  the  ftveral  bafes  and  perpendiculars,  on 
the  fame  fcale  that  the  map  was  laid  down  from ;  find 
the  content  of  each  triangle  and  trapezium,  by  the  pre 
ceding  problems,  and  their  fam  will  be  the  area  of  the 
rnap. 


TO  FIND,  THE  CONTENT  OIF  LAND, 


EX-AMPLE     i. 

Required  to  lay  down  a  Map  of  30  Perches  to  an  inch, 
from  the  following  Notes,  and  find  the  .Content. 

Beginning  at  a  done,  corner  of  A  B's  land  ; 

From  thence, 

N.  43°  I  E.  10.51  chains,  to  a  flake;  thence, 
S.  54°  -JE.  14.2:0  chains,  to  a  fapling,  corner  of  CD's 

landj  thence, 

S.  49°  \  W.  13.45  chains,  to  an  oak  tree  ;  thence, 
N.  43°  J  W.  13.75  chains,   to  the  place  of  beginning-* 

Ch.  Per. 

N.  43°  |E,  10.51  =  42.04 
S.  54°  \  E.  14.^0  =»  56.80 
S.  49°  \  W.  13.45  =  53-8° 
N.  43°  i  W.  12.75  =  5li°° 

Perches. 
Perpendiculars  J  ^5-4 

66.4 
Bafe        7.5 

1)4980.0  double  area, 
4,0)349^0 


(See  the  following  figure.) 


120       TO  FIND  THE  CONtENT  6*  LAND* 

N 


X    A    M    P    L    E       2. 


The  fallowing  Nctes  are  propofed  to  lay  down  a  Map 
of  40  perches  to  an  Inch,  and  find  the  Content, 


Ch.          Per. 

1.  S.  40°  W.  17.50  =  70. 

2.  N.  45°  W.  221.25  =  89* 

3.  N.  36  E.     31.25  =   125. 

4.  North  13.60  =    54.4 

5.  S.  81°  E.    4^.50  =  186, 

6.  S.  8*  W.  34.25  -  137- 


Weil 


3M5 


130.2 


TO  FIND  THE  CONTENT  OF  LAND, 


.  In  Practical  Surveying,  it  is  neceffary  to  particularize  etfe- 
ry  corner,  and  on  whom  each  line  bounds  ;  which,  to  avoid 
prolixity,  I  omit  in  this  treatiie. 

In  the  following  Maps,  I  fliall  number  the  bafes  of  the 
Several  triangles  and  trapeziums. 


I 

3 

4 

Bafes. 
.     108.3 
.     125. 
.     1  66. 

•     233. 

Perpeii. 

58. 
92. 
IT. 

91.  t 

no.  j 

JDouble  Area* 
6281.4 
11500.0 
1826.0 

46833.0 

1)66440.4 

4,0)3322,0^.2          *• 

Area 

R 

4)830   20 

A.  207  2  2oAnfwer, 

tO  FIND  THE  CONTENT  OF  LAND. 


EXAMPLE     3. 

The  following  Notes  are  propofed,  to  lay  down  a  Map 
of  40  Perches  to  an  inch,  and  find  the  Area; 


Chains. 

Perches 

I. 

N.  75°        E. 

13.70 

._,, 

54-8 

a.     N.  2,0°  A  E. 

10.30 

'.-.    _ 

41.2 

3- 

Eeaft 

16.20 

-- 

64.8 

4- 

S.  33° 

i  w. 

35-30 

^^. 

I4I.Z 

5- 

S.  76° 

w. 

1  6.00 

.      .    .. 

64.0 

6. 

North 

9,00 

~—  ^. 

36.0 

*]. 

S.  84° 

w. 

1  1.  60 

•^. 

46.4 

8. 

N.  53° 

i  w. 

1  1.  60 

—  ^ 

46.4 

9. 

N.  36° 

IE 

19.20 

• 

76.8 

10. 

N.  22° 

14,00 

-  : 

56.0 

11. 

S.  76°  |  E. 

12.  OO 

—  ^. 

48.0 

12. 

s.  15° 

W. 

10.85 

_^ 

43-4 

13. 

S.  16° 

1  w. 

IQ.I2 

=ss 

40.48 

TO  FIND  THE  CONTENT  OF  LAND.      123 
Bafes. 


i. 

59-° 


9°-°} 


86.0 


Pel-pen.' 

Double  A.rea, 

,33-51 
29.9  > 

35- 

4787.90 
2065.00 

49-3  1 
40.0  \ 

."803^.00 

*T                  J 

3,6.3 

1906.75 

26.0 

2236.00 

20.0") 
42.  2  J 

7003,7* 

44-0 

6212.80 

7-      I4I-3 

8.       85.6  *7->5  ^35±^_- 

-1)34603- *7_ 

4)43^2^~ 
Acres  io8~o  21  Anfw. 

EXAMPLE     4. 

Required  to  lay  dot\rn  a  Map  of  20  Perches  to  an  Inch, 
from  the  following  Notes,  and  find  the  Area. 


Ch,         Perches, 

I. 

S.  62°      W. 

7-57  a-  3°-*S 

2. 

N.  43°  *W.' 

5.89  ^  23.56 

a. 

North 

5.82  ==,  23.28 

•7 

4- 

N.  33°  JW. 

8.83  «  35.33 

*>• 

N.  48   E. 

4.81  —=  19.24, 

6. 

N.  12   E. 

4.66     =55     l8.64 

7. 

R  62°   |E. 

5.27    -a    2T.o8 

8. 

S.  6°  |  E. 

5.60    -a    22.40 

Q- 

S.'  40°  4  E. 

5.87    =    23.48 

s 

10. 

Eaft 

6.54   —    20.l6 

II, 

North 

5,52     5=    22.08 

12. 

N.  68°  *  E. 

2.io  s=  12.40 

T3- 

S.  30°  E. 

7.90   aa-   3I.6O 

14. 

S.  23°x  W. 

.   8,80    =    35.20 

S.  31°  IF, 

6-42    ==    25.68 

16, 

S,  ^-o°  W, 

8,40    =    33,6o 

N,  44°  W, 

7,04  -a   28,l4 

TO  FIND  THE  CONTENT  OF  LANJX, 


This  figure  js  tnrn'd  up-nde  down 


Safes. 

Perp. 

Double  Area<f 

No,  i, 

24,6    | 

17$  I 

873,30 

2, 

42,6      i 

15-8 

673,08 

3> 

52,0  j 

21,01 

22,2  J 

2246,40 

4, 

43,4 

8,5 

368,90 

5, 

73,o   I 

26,0?  . 

35H,30 

6, 

59,2  ? 

24,4? 

2812,00 

j  • 

23,1  $ 

7> 

46,0   £ 

•20,7  ? 

IQ73,4© 

8, 

35,7 

25,  i 

896,07 

9? 

35)2  1 

8SJ 

985,60 

i)  14340,05 

4)0)71710.02 

• 

4)179   10 

Acres  44  3   loAnfw 


TO     FIND     THE 

CONTENT  OF  LAND, 

B    Y 

CALCULATION. 


THE  foregoing  method  of  dividing  a  map  into  Tri 
angles  and  Trapeziums,  although  it  appears  to  be 
demonftrably  true  in  theory,  it  is  not  to  be  depended  on 
in  pra&ice,  where  accuracy  is  required  ;  for  a  map  may 
be  fo  divided  feveral  ways,  and  will  generally  give  as  ma 
ny  different  areas  ;  therefore  I  fhall  not  enlarge  upon  it 
here,  but  proceed  to  fliew  how  the  true  Area  may  be 
found,  by  difference  of  latitude  and  departure. 

DEFINITIONS. 

1.  Meridians  are  North  and  South  lines  fuppofed  to 
pafs  through  every  ftation,  parallel  to  each  other. 

2.  .The  difference  of  Latitude,  or  Northing  or  South 
ing  of  any  line,  is  the  diftance  that  one  end  of  the  line  is 
North  or  South  from  the  other — Thus  in  the  annexed 
fgure          •    .  N 


B 


126      TO  FIND  THE  CONTENT  OF  LAND. 

Suppofe  N  S  to  be  a  meridian  line,  pafllng  through  the 
point  A,  of  the  line  AB  ;  then  is  AD  the  differenpe  of 
latitude  or  fouthing  of  the  line  AB. 

3.  The  Departure  of  any  line,  is  the  neareft  diftance 
from  one  end  of  a  line  to  a  meridian  palling  through  the 
other  end ;  thus  DB  is  the  Departure  or  Wefting  of  the 
line  AB, 

Reverfe  this  line,  and  call  it  BA  ;  then  will  BCbe  the 
Difference  of  Latitude  or  Northing  of  the  line  BA,  and 
CA  the  Departure  or  Eafting  of  the  fame  line. 

4.  That  meridian  which  pafies  through  the  firft  Ration, 

is  called  the  firft  meridian. 

/ 

The  meridian  diftance  of  any  line,  is  the  diftance  there 
of  from  die  laft  meridian. 


POSITION. 

In  every  furvey,  which  is  truly  taken,  the  fums  of  the 
Northings  and  Southings  will  he  equal ;  and  the  fums  of 
the  Eaftings  and  Weftings  will  be  equal. 

For,  if  I  depart  from  any  place,  fuppofe  A,  in  the  an 
nexed  figures,  it  is  evident,  that  when  I  return  to  the  fame 
fpot,  I  iriuft  have  made  as  much  Northing  as  Southing,  and 
Eafting  as  Wefting,  let  my  traverfe  be  ever  fo  irregular. 

(See  the  following  Figures.) 


TO  FIND  THE  CONTENT  G-F  LAND, 


ffo  :ake  out  of  the  Tables  of  Latitude  and  Defr.  • 
the  Difference  of  Latitude  and  Departure,  ans\. 
to  any  Course  and  Distance. 

R    U,   L    E. 

If  the  integral  number  exceedstnot  100,  it  is  found  iil 
ttie  right  and  left  hand  columns,  marked  Dis't.  And  if 
the  degrees  be  lefs  than  45,  they  are  found  at  the  top  of 
the  page  j  and  in  the  columns  marked  Lat*  and  Dep*  is 


TO  FIND  THE  CONTENT  OF  LAND. 

the  latitude  and  departure  aniwering  thereto  ;  but  if  the 
degrees  exceed  45,  they  are  found  at  the  bottom  of  the 
page,  and  the  latitude  and  departure  in  the  columns  fo 
marked  at  the  bottom.  Then,  oppolite  to  the  given  di- 
flance,  and  under,  or  over  the  given  degrees,  will  be  ths 
Latitude  and  Departure  required.  And  if  a  decimal  num 
ber  be  annexed,  proceed  with  it  as  if  a  whole  number, 
only  obferve,  in  taking  out  the  difference  of  Latitude  and 
Departure,  to  move  the  decimal  point  as  many  figures 
to  the  left,  as  are  in  the  given  decimal :  and  thefe  laft 
numbers,  added  to  the  former,  will  be  thofe  fought  -,  but 
if  the  diftance  -exceeds  100,  it  muft  be  taken  out  at  two 
or  more  times,  and  the  refults  added  together.* 

EXAMPLES. 

Suppofe  the  courfe  to  be  N.  34°  £  E.  and  diftance  14*64 
chains. 

Lat.  Dep* 

Oppofite  to  14,  and  under  34° -|,  I  find  11.54  7.93 

Oppofite  to  64,  and  under  the  fame  deO 

grees,  moving  the  decimal  point  two  J-     00.52,     0.36 

figures  to  the  left,  I  find  J 


Gives  the  number  fought                                 1-4.06  8.29 

Bearing  S.  53°  £  W.  Diftance  26.17  chains. 

Lat.  Dep. 

Oppofite  to  26,  and  over  53°  £,  I  find       15.56  20.83 
to  17,  moving  the  point  two") 

figures  to  the  left,  I  find     J     °°'10  CO>14 

The  numbers  required,                                   15,66  2O,of 


TO  FIND  THE  CONTENT  OF  LAND.      129 

Bearing,  N.  28°  |W.     Diftance,  146,8  perches. 

Lat.  Dep, 

Oppolite  to  100,  and  under  2.8°  |,  I  find     87,67  48,10 

to  46,  in  the  fame  columns,  I  find   40,33  22,13 
to  8,  moving  the  point  one  figure  1 

i        i    r   i         j  5-OO-.7O       OO,70 

to  the  left  hand,  J      '' 

•Give,  as  required,  128,70     70,61 

If  the  given  diftance  be  lefs  than  10,  and  only  one  de 
cimal  figure,  then  the  difference  of  latitude  and  departure 
may  be  tak£n  at  one  view,  by  finding  the  two  figures  in 
the  fide  column,  as  if  they  were  a  whole  number ;  and 
in  taking  out  the  latitude  and  departure,  move  the  deci 
mal  point  one  figure  to  the  left. 

Suppofe  the  -bearing  to  be  S.  18°  |E.     Diftance  7,40 

chains. 

Lat.       Dep. 
Oppofite  to  74,  and  under  1 8°  |, -moving  ") 

the  point  one  figure  to  the  left,  I  find   J    ' "  *37 

Thus  proceed  with  every  Courfe  and  diftance  in  the  fur- 
vey,  and  place  the  numbers  in  their  refpe&ive  columns* 
in  tables  ruled  for  that  purpofe,  as  in  the  Examples  fol 
lowing.  Then  add  up  each  column,  and  if  they  balance, 
as  mentioned  in  the  preceding  pofition,  the  work  is  right* 

But  in  real  pra&ice,  it  but  rarely  happens,  that  the 
columns  of  latitude  and  thofe  of  departure,  will  balance 
on  firft  being  added  up,  for  little  inaccuracies  will  arife, 
both  in  taking  the  obfervations,  and  in  chaining ;  to  adjuft 
which,  Observe^ 

s 


TO  FIND  THE  CONTENT  OF  LAND, 


That  in  fmall  furveys,  if  the  difference  amounts  to- 5  li-nits 
for  every  ftation,  there  mult  have  been  fome  error  com 
mitted  in  taking  the  farvey  ;  and  the  beft  way  to  re&ify 
it,  will  be  by  a  re-furvey  oil  the  ground,  or  at  lead  fo 
rmica  of  it  as  will  difcover  the  error.  But  if  the  differen 
ces  be  within  thefe  limits,  the  work  may  be  balanced,  by 
adding  one  half  of  the  differences  to  the  numbers  in  the 
lefs  columns,  and  fubtra&ing  it  from  thofe  in  the  greater, 
in  fuch  a  manner,  that  the  numbers  may  be  altered  nearly 
in  proportion  to  their  correfponding  diftances,  as  in  the 
annexed  E  x  A  M  P  L  E. 

i. 


i 


i  f 

I  .^ 

~  cr» 


PJ 


W 


r 


t 


tef 


TO  FIND  THE  CONTENT  OF  LAND.    .  131 

Having  found  the  .difference  of  latitude  and  departure 
.to  every  courfe  and  diftance,  .and  balanced  the  columns, 
if  neceffary,  then  find  the  meridian  diftances,  by  choofmg 
Inch  a  place  in  the  columns  of  Eaftings  or  Wettings,  as 
will  admit  of  a  continual  double  addition  of  the  one,  and 
fabtra&ion  of  the  other ;  and  this  will  end  in  o,  ,o,  or  a 
cipher,  if  the  additions  and  iubtra&Lons  be  right ;  becaufe 
there  is  juftas  much  added  as  fubtra&ed,  which  will  be 
come  eafy  and  familiar  by  a  little  pra&ice,  and  inftru&ion 
•from  the  teacher. 

Then  multiply  each  upper  meridian  cliflance  into  Its  re- 
ipe&ive  Northing  or  Southing,  and  place  the  products 
in  their  refpc£live  columns  of  North  or  South  area,  and 
half  the  difference  between  the  fums  of  thefe  columns  will 
be  the  area  of  the  map,  in  fuch  meafure  as  the  diftances 
were  taken  in.  As^xemnliued  in  the  folio  wing  exam 
ples. 

I  (hall  now  proceed  to  find,  by  calculation,  the'  area  of 
each  of  the  preceding  furvcys. 

Note.  In  the  following  example,  the  rciu.TT.ic  o.Vdfrerenco 
of  latitude  and  departure,  will       I  on  firil  ad- 

addinff  UD. 


E  x  A  M  P  1. 


TO  FIND  THE  CONTENT  OF  LAND. 


EXAMPLE       I. 


00 

pa 


OO 

on 
vi 

Ox 
O 


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VJ 


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w 

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$ 

1 

0 
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o 

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sa 

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0 

CO 

p 

TO  i-,.  D  THE  CONTENT  OF  LAND. 


en 


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Os 


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.3A.  •    TO  FIND  THE  CONTENT  OF  LAND, 

Map  of  the  preceding  Calculation* 
C  B          G 


D  E  M  O  N  S  T  R  A  T  I  O  N. 

Ab  or  DC,  is  the  eaft  departure  of  the  firft  diftancq 
AC  ;  and  AD  or  bC  the  north  difference  of  latitude,  gh 
the  eafl  departure  of  the  fecorid  diftance  Ch  ;  and  Cg  = 
DE,  the  Jouth  difference  of  latitude,  PO  the  weft  depar 
ture  of  the  third  diftance  h"0,  and  VO  =  EF  the  fouth 
tlifTerence  of  latitude,  OP'  the  weft  departure  of  the  laft 
<liftaace  OA,  and  FA  the  north  difference  of  latitude ; 
and  AD  x  DC=the  are  of  Ab'CD,  and  DC-f-DC+gh-a 
DG  a-  El,  and  El  x  DE  =  the  area  of  EIGD  ;  and 
KI  4-  gh  =  EK,  and  EK  —  PO  •=  EL  =.  FT,  and 
I'T  X  FE  =  the  are  of  FTLE,  and  T;T  —  PO  ==  OF 
sa  FO,  and  FO  x  FA  =-  the  area  of  FOrA. 

It  is  fufficiently  clear,  that  the  fouth  areas  take  in  thofc 

of  the  north,  and  that  the  ium  of  the  north  areas  is  equal 

to   the    fura  of  the  parallelograms  BGIh,   and   hLTP; 

therefore  the  faro  of  the  north  areas  taken  from  that  of 

;bnth,  leaves  the  area  of  the  parallelogram  DBPF, 


TO  FIND  THE  CONTENT  OF  LAND.        135 

••» 

which  is  double  the  area  of  the  map.  For  (by  Pofitions 
^  and  3)  a  triangle  is  equal  to  half  a  right  angled  paral 
lelogram,  made  by  the  bafe  and  perpendicular  height  oF 
the  triangle ;  fo,  alto,  mull  a  trapezium  be  equal  to  hall" 
a  right  angled  parallelogram,  made  by  the  bafe,  and  heigha 
of  the  fum  of  the  two  perpendiculars. 

Now,  ii  a  line  be  drawn  from  the  point  A  to  h,  and- 
from  the  points  C  and  O,  let  fall  perpendiculars  on  that 
line  or  bafe,  then  the  map  is  a  Trapezium  (fee  the  fame 
figure  1 20)  and  the  parallelogram  DBPF,  equal  to  the  two. 
parallelograms  made  on  the  bafe  Ah,  one  or  them  being, 
the  height  of  a  perpendicular  from  C,  and  the  other  of  one 
from  O.  The  fame  demonftration  will  hole!  good  on  like 
principles,  where  the  Meridian  diftance  is  Wed,  and  the 
South  areas  taken  from  thofe  of  the  North,  leave  the  dou 
ble  area  of  the  map.  And  the,  fame  of  any  map  or  fj££- 
vey. 


E  X  A  M  P  L 


TO  FIND  THE  CONTENT  OF  LAND< 

EXAMPLE     2. 


a 


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TO  FIND  THE  CONTENT  OF  LAND. 
Proved  by  making  West  Meridian  Distance, 


137 


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N>      00 

4s.    O 

b*.          yjK 

**"• 

*" 

* 

b 

> 

P 

•t 

If 

SN% 

to 

w 

^M 

as 

OO 

ON 

»^    o 

00 

*vj 

)M 

^o 

CO 

M 

ON 

to 

° 

00 

NO 

O 

M 

^J 

00 

M 

O    OO 

\o  *<r 

00 

o 

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to 

00 

ON 

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ON 

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o 

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o 

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M 

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H 

00 

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oo 

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-^ 

Ol 

i 

H 

£t 

VD 

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V 

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4 

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u. 

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J 

•^ 

TO  FIND  THE  CONTENT  OF  LAND. 


To  make  a  Map,  from  Difference  of  Latitude  and 
Departure. 

RULE. 

i.  Draw  a  meridian  line  as  N  S,  and  aflume  a  point 
therein,  for  the  firft  ftation,  as  I,  through  which  draw  a 
line  perpendicular  thereto  both  ways,  ts  WE. 

3.  Lay  the  difference  of  latitude  of  the  firft  diftance, 
from  faid  point,  on  the  meridian,  upward,  if  N©rth,  and 
downward,  if  South,  as  from  A  to  i  ;  and  that  of  the  fe- 
cond,  from  i  to  2,  ;  and  the  third  from  2  to  3,  &c.  1^ 
the  laft  coincide  with  the  firft,  it  denotes  its  re&itude. 
In  like  manner  lay  the  departures  on  the  line  WE,  to 
wards  the  right  hand,  if  Eaft,  and  towards  the  left,  if 
Weft,  as  from  A  to  i,  from  i  to  a,  from  3  to  3,  &c.  as 
in  the  annexed  figure 

3.  With  the  diftance  from  A  to  I,  on  the  line  NS,  and 
one  foot  in  i,  on  the  line  WE,  defcribe  an  arch  upward, 
if  North,  and  downward,  if  South,  as  at  B,  and  with 
the  diftance  from  A  to  i,  on  the  line  WE,  and  one  foot  in 
i,  on  the  line  NS,  crofs  the  faid  arch  in  B,  the  place  of 
the  fecondftation;  and  fo  for  the  ad,  3d,  4th,  &c.  which 
joined  with  lines,  will  complete  the  map. 


MAP 


TO  FIND  THE  CONTENT  OF  LAND.      139 


MAP    of  tie  preceding  Calculation* 


I4o    TO  FIND  THE  CONTENT  OF  LAND. 
EXAMPLE     III. 
West  Meridian  Distance. 


No.  Bearings,  Dift 

N.L.S.  L.JE.D 

W.D 

W.M.D 

52.84' 
39-6o 

N.  Area. 

IN  75  E 
a'Naof  E 

Enaiiji 
:3-?c 

3-54 

13.24 
3.60 
16.20 

187.0536 

10.30 

9.65 



36.00 
32.40 

347.4000 

3'    Eaft 

«>33*W 

5S  76  W 

16.20 

16.20 
oo.oo 

35-3° 

29.44 

19-49 

19.49 
38.98 

16.00 
9.00 

3-87 



J5-52 

54.5° 

70.02 

6   North 

9.00 

70.02 

630.1800 

7 

8 

~9 

S   84  W 

ir.6o 

1.20 

11.54 

81.56 

93-1° 

709.5627 

N53|W 

ii.  60 

6-93 

- 

9.29ii2l39 
y|in.68 

N36f  E 

N22i£ 
S  76  £E 
S  15    W 
Si6|W 

19.20 

i5-3^ 

. 

11.48 

1  00.20 
^d8.72 

1541.0.760 
1077.8448 

10 

ii 

12 

$ 

14.00 

I2-93 

5-36 

£.3^6 
78.00 

66.32" 
54-64 

2.00 

2-75 

11.68 

0.85 

O.I2 



0.48 
9.69 



2.81 
2.91 

••57-45 

00.20 

63-^7 
66.08 

57-43 

7.4361.56 

61.56 

4493.1171 
227y.i459 

S. 


97.872* 


182.3800 


2279.1459 


A.         R.        P. 

Area  j  10  :    a   :   3  a  nearly. 


A.I  10,6985  6 
4 

R.      2,79424 

40 

P.      31,76960 


TO  FIND  THE  CONTENT  OF  LAND.    141 

The  EXAMPLE, 
By  East  Meridian  Distance. 


<4o  |  Bearings 

IN  75  E 

Dift. 

13-70 

jN.L.fS.  S.  E.  D 

JW.D 

E.M.D   N.  Area. 

s.  Area 

3-54 

13  3.; 

72.0? 
75.6J  " 

308.2936 

aNaoiE 

10.30 

9-65 

3.60 

730.3120 

3      Eaft 

.6.0 

16.20 

95-4B 
11168 

72.70 

4S33*W 

35.30 

29.44 

19.49 

2714.0736 

5  S  76  W 

I 

1  6.00 
9.00 

3-87 

15.53 

57.i8 
41.66 

221.2866 

North 

9.00 

41.66 

374.9400 

7 
8 

S  84  W 

ii  60 

1.20 

ci-54 

30.12 
18.58 

36.1440 

•*^  0  3-4- 

1  1.  60 

6-93 

9.29 

o.oo 

64.3797 
176.5624 



9 

N  36!  E 

19.20 

15.38 

11.48 

11.48 

10 

N»iE 

14.00 

12.93 

5.36 

28.32 
33.68 

366.1776 

tils  76|  E 

I2.0O 

3-75 

n.68 

124.7400 

.57-04 

12 

S  15  W 

10.85 

10.48 

2.81 

54.53 

5  1.43 

568  3304 

- 

St6|;W 

10.12 

A. 

9.69 

2.91 

48.51 
45-6o 

470.06  9 

5743 
R. 

57-43 
P 

61.56 

61.56 

1920.6653  4I34'  3  •* 
|i920.6653 

•1)2213.9712 
A  110,6.9856 
4 

Area  no   :    a    :    32  nearly. 


i42    TO  FIND  THE  CONTENT  OF  LAND. 

EXAMPLE     IV, 


No 

Hearings 

Did. 

N  L| 

S.L. 

3-56 

E.D.  W.D. 

W.M.D 

29.50 

N.  Area 

171.7824 
257.7096 
361.8176 

I 

2 

3 
4 

5 

S  6*  W 

N43*W 

7-3  T 
c.89 



6.68 

36-18 

4-i? 

4-05 
4.88 

4o,»a 
4428 

North 

582 

5-8» 



44.28 

'49-  1  6 
34.04 

N35-IW 
N  48  E 

8.83 

7.36 

4.81 

3-" 

3-57 

30.47 
46.90 

45-9* 

162.5154 

6 

7 

1 
9 

N  JZ   E 

4,66 

4-55 

0.96 

209.0270 
97.9290 

44-9« 

N6z|E 

5-  *  7 

1-43 

4.68 
0.63 



40.30 
35-6z 

S  6|E 

S4of  E 

5.60 
J.8; 

5-56 

3499 
3>36 

30.55 
a6.'/4 

4-46 

3-8>- 

10 

Eaft 

6.34 

552 
3.10 

6,54 

20.20 
iT66 

ii 
12 

North 

5-52 



2.88 



13.66 

75.403^ 

N68-*;  E 

I.J3 

i 

10.78 

ia-3970 

7.90 

13 

S3oE 

7.90 

6.84 

3-95 

395 

o.oo 



14 

S  23   W 

8.8c 

8.10 

• 

3-44 

3-44 
6.88 

15 
1  6 

S  3l|E 

6.42 

5-47 

3-35 

3-53 
0.18 

850   W 

8.40 
7.04 

5-40 

6.43 
489 

6.61 
1304 

'7 

N44  W 

i-°7 

17-93 
az.Si 

90-9051 

39-39 

39-39 

30-37 

30.37 

1439.4840 

?4<T.7O2f 

05,0200 


194,5444 


^7,0180 
27,8640 


19,3091 
35,6940 


545,70*5 


A,        R,        P, 

Area  44  :     »  :    30,25* 


A.  44,689075 


^ 

R.     2,756300 
_  40 
I',    30,^5  aooo 


TO  FIND  THE  CONTENT  OF  LAND.      143 

The  same  Example    calculated  with   East   Meridian 
Distance. 


No  !  Bearin.es  Dift  1 

f.L.    S.L. 

E.  D. 

AT.D 

!.M.  D'N.    Area'  S.   Area 

J 

5  6a  W 

du 
7-57 

3-56 

.6.6. 

24-54 

9.76 

87,3624 

a 

<43*W 

5.89 

4-27 

4.05 

58.9687] 

3 

North 

5.82 

5.82 

9.76 

56.8032 

4 
5 

\j  o«£\V 

8.83 

7-36 

3-57 

4.8C 

4.88 

0.00 

35.9168 

N  48  E 

4-81    3.22 

* 

Ml 

7.14 

11-4954 

— 

6 

N  12  E 

4.46 

4-55 

2.43 

0.96 

9.06 

36.8550 

7 

NfiziE 

.27 

4.68 

13-74 

I  S.  42 

33.3882 

8 

S6*  E 

^ 

0.63 

IQ.Q5 

19.68 

^05.9x8, 

( 

S4o*E 

5-«7 
6.54 

5-52 

4.46 

3.81 

2  7.4.0 



104.7654 

27.30 

10 

Eaft 

6.54 

3i^4 
40.38 

II1  North 

5-53 



40.38 

222.8976 

1      ' 

12 

N  68-|  E 

3-iq 

**, 

2.88 

43-^> 
46.14 

49-7490 

13 

S  30  F 

7.90 

6.84 

3-95 

5To4 

341.6156 

14 
I. 

SajW 

S.8c 

\ 

8.  ic 

3-4^ 

50.60 
47.16 

1  40^.8600 

6.4: 

5-4' 

3-3f 

5°-5\ 

it 

*~ 

X 

is  50^ 

8.40 

5-4 

j     **              . 

183.077" 

256.1220 

•  N  44  W  7.0^ 

A 

Area  4 

I    5.0- 

4-3 

36.  TT 

39-3 

I 
t   '•   * 

39-3 

L 

:    3C 

3°-3 
I*. 

3^-3 

i 

A 
R 
P 

-,  i582-933l 
63<M  ^16 

.4n,;5oo75 
4 

40 

*<4      TO  FIND  THE  CONTENT  OF  LAND. 

EXAMPLE     5. 

This  example  has  an  inacceflible  boundary,  occafioned 
by  the  points  of  a  lake  projecting  into  the  land,  between 
the  3d  and  4th  corners ;  to  furvey  which,  I  take  the 
Field  Notes  as  follows,  and  in  perches,  as  fome  furvey. 
©rs  are  in  the  practice  of  fo  calculating  their  furveys. 


Per. 

I. 

North 

37-9 

3. 

N.    85    E. 

36.0 

3-  14. 
15- 

S.  25    W. 
S.     2  E. 
S.  26  E. 

25.0' 

35-° 
2,0.0 

4.      6. 

S.  85  W. 

60.0 

5-     7- 

N.  3  W. 

40.0 

6.      8. 

Eait. 

26.8 

Take  the  difference  of  latitude  and  departure,  for  the 
three  devious  courfes  and  diftances,  and  what  they  want 
of  balancing,  will  be  the  difference  of  latitude  and  depar 
ture  for  the  diflance  from  the  3*d  to  the  4th  corners, 
with  which  find  the  bearing  and  diftahce,  as  under  fpeci* 
fied. 


No 

Searings. 
S.  25  W. 

DHL 

N.L. 

S.  L.i 

E.  D. 

W.D. 

3 

25.0 

22.7 

10.6 

4 

S.  2E. 

35-o 

35-° 

1.56 

5 

S.  26  E. 

20.O 

18.0 

8.8 

N.  E. 

75-7 

0.6  I 

75.7    75.7    10.6     ic.6 


TO  FIND  THE  CONTENT  OF  LAND.      145- 

Note. .  When  calculations  are  made  in  perches,  it  is  ufual 
to  retain  but  one  decimal  figure :  \and  when  the  fccond 
is  more  than  five,  to.increafe  the  firit  one  more. 

To  fiad  ,the  bearing  from  the  3d.  to  the  4th.  corner*  , 

As  dmw — „  of  latitude  3*       75-7?.       1.87910 

Is  to  radius  90* 

So  is  departure  4a  c.6P.          — 9 

9.77815 
1.87910 

To  Tangent  bearing  o°  27*  7.r899©5 

From  the  4th  to  the  3d  corner,  N.  o°  27'  E. 
From  the  3d  to  the  4th  coiner  S.  o°.  27'  W. 

To  find  the  diftance  from  3d  to  4th  coi^ier^  , 

As  radius  9°°  10.00000 

Is  to  difference  of  latitude  33        75.7       1.87.910 
So  is  fecant  bearing        0.27  10,0000 1 


To  the  diftance  75.7-: 
The  T-raverfe  will  nowftand  as  in  the  following  page, 
H 


546      TO  FIND  THE  CONTENT  OF  LAND. 


No 

Bearings. 

Dift.  Per. 

N.  L. 

3.   L. 

E.  D. 

WJX 

i 

2 

3 

North. 

37-9 

37-9 

N.   85°  E. 

36.0 

3-1 

35-7 

S.  27'  W. 

75-7 

75-7 

0.6 

4 

S.  85  W. 

60.0 

5.2 

^9-8 

jr 

-NT      j      »v. 

40.0 

39-9 

2.1 

6 

Eaft. 

A  „_               _    A 

26.8 

T»           n 

26.8 

62,5 

80.9 

80.9 

62.5 

Area  M A.  3R.  38.91?. 
Jtfote.  The  calculation  is  emitted,  to  exercife  the  learner, 

N 


Jo  L 


-\ 

V 

j  ^ 

I    !\ 

i 
1 

* 

1       Jl 

TO  FIND  THE  CONTENT  OF  LAND.      i4y 

EXAMPLE    6. 

In  the  following  furvey,  the  laft  courfe  and  diftance  is 
•omitted  to  be  taken  ;  but  it  is  required  to  be  found,  and 
allo  the  area  of  the  land  inclofed. 

RULE. 

Find  the  difference  of  latitude  and  departure  as  before," 
for  the  leveral  courfes  and  diftances  taken,  and  what  they 
want  of  balancing,  will  be  thofe  of  the  clofmg  line,  which 
find  by  Gafe  6  and  7,  Right  Angled  Trigonometry. 


CO 

HH 
HH 

O 
ffi 

Q 

W 

•n 

o 

o 

O 

> 

& 
g 

0% 

yj 

CO 

CO 

to 

£ 

25 

% 

^ 

teJ 

Cs 
O 

0 

0 

M 

OJ 
HfH 

•w 

Os 
Ho 

w 

i 

w 

z 

eanngs. 

w 

Os 

00 

00 

M 

O 

SO 

>T 

SO 

i 

£ 

* 

£ 

* 

£ 

0 

Os 

^J 

P 

•t 

b 

- 

+ 

bo 

?t 

H 

* 

M 

Os 

E^ 

Os 

Os 

ocr 

0! 

UQ 

O 

^ 

10 

s 

r1 

M 

M 

Os 

so 

ia 

w 

oo 

Os 

VD    • 

^ 

u> 

•s 

b 

o 

u 

OO 

^ 

Os 

X 

M 

G 

TO  FIND  THE  CONTENT  OF  LAND. 

To  find  the  bearing. 

As  difference  of  latitude  Ha      6.10         0*78533 
-  Is  to  radius  90  10.00000 

So  is  departure  Aa  10.62 


Ta  tangent  bearing  HA  60°  07' 


To  find  the  Diftance. 
radius 


9°' 


IO.OOOOO 


Is  to  difference  of  latitude  Ha     6.10 


So  is  fecant  bearing 


Te<the  diflance  HA 


60°  07'          10.30256 
11.08789 

IO.OOOOO 


1.06789 


-Note.  Obferve  the  above  proportion,  in  finding  the  beam 
ing  and  diftance  of  all  lines  required,  as  above. 


AW  A 


TO  FIND  THE  CONTENT  OF  LAND,      149 
THE      MAP. 


I? 


G 


150      TO  FIND  THE  CONTENT  OF  LAND. 


E.  -X    A    M    P    L    E      7. 

In  the  following  furvey,  the  corner  at  A  is  inacceffibloj 
occafioned  by  the  overflowing  of  water ;  but  it  being  a 
tree,  it  can  be  feen  from  the  adjacent  corners  B  andL;  I 
therefore  fet  my  inltrument  at  B,  and  take  the  bearing  to 
A,  which  I  find  to  be  S.  51°  \  E.  This  I  reverfe,  and 
place  it  as  the  fir  ft  bearing  in  my  field  book,  viz.  N.  51° 
i  W.  then  proceed  and  take  the  icveral  bearings  and  di- 
fbnces  to  L;  and  from  L,  I  find  the  bearing  to  A  is  S^ 
20°  A  W.  which  I  put  for  the  laft  bearing  in  my  field  book, 
as  under  exemplified* 


Stations.  ' 

Bearings. 

Dift. 

Ch 

N.  L. 

S.  L. 

E.D. 

W.  D. 

AB 

N.  51  JW. 

EC 

S.45  iW. 

15.16 

10.62 

1  0.8  1 

CD 

N.  50.  W. 

22.10 

14.10 

16.93 

BE 

North. 

18.83 

18.83 

"EF 

N.  48  E. 

2,'2.6c 

15.12 

16.79 

FG 

N.  25  A  W. 

20.17 

18.20 

8.68 

OH 

haih 

26.57 

26.57 

KI 

3.   30  -£  E. 

22.86 

19.70 

ii.  60 

IK 

S.    44  W. 

15.04 

>  10.82 

10.45 

KL 

S.  47  E. 

28.55 

10.47 

20.88 

LA 

S.    30  £W. 

The  learner  fnould  fet  down  all  the  work  in  full. 


TO  FIND  .THE  CONTENT  OF  LAXD.       15* 

The  difference  of  latitude  and  departure  being  found  for 
the  feveral  courfes  and  diftances  as  above,  and  the  co 
lumns  added  up,  there  will  be  wanting  5.74  fouthdiffer- 
cnce  of  latitude,  and  2.8.97  v;;--  departure,  to  make  the 
columns  balance*  as  before  directed-,  which  are  the  dif 
ference  of  latitude  and  departure! from  L  to  B  ;  with 
which,  as  in  the  foregoing  examplf,  the  bearing  of  LB  is 
found  to  be  8.78°  48 'W.  an^t ':  .,  .-.bains  ;  then, 

in  the  triangle  ABL,  there  qife  g'fven  the  llde  LB,  and 
by  the  bearings  of  the  lines,  the!  angles  ABL  49°  57', 
ALB  58°  i8y,  BAL7i°,45/,  to  find  the  ether  fides;  and 
by  Cafe  i,  Oblique  Angled  Trigonometry,  AB  is  found 
to  be  2,6.47  chains,  whickfet  in  its  proper  place,  oppofite 
its  bearing,  and  the  fide  'LA  2,3.82,  chains,  which  place 
oppofite  to  its  bearing  ;  find  the  difference  of  latitude  and, 
departure  to  thefe  diilances,  and  proceed  as  before,  to 
find  the  area  of  the  furvcy,  which  is  2:44 A.  3^» 

(See  the  following  figure.) 


THE     MAP. 


TO  FIND  THE  CONTENT  OF  LAN0. 


THE    MAP. 


N 


O    F 

O    F    F  -  S    E    T    S. 

OFF    SETS  are  perpendiculars   meafured  froift 
the  angular  points  of  the  land,  to  the  ftationary 
diftance  on  either  fide  thereof;  to  do  which,  obferve  the 
following 

R    U    L    E. 

Rule  a  table,  as  hereafter  exemplified ;  take  the  bear 
ing  of  the  line  from  which  ofF-fets  are  to  be  made,  and 
from  this  line  make  off-fets  at  right  angles  to  eath  angu 
lar  point  on  either  fide  >  fet  the  diftance  to  each  off-fet 
under  the  head  of  Bafe,  and  the  diftance  of  each  off-fet? 
under  that  of  Perpendicular. 

Then,  to  find  the  area  of  thefe  ofF-fet3$ 

Set  the  firftbafe  oppofite  to  ftation  I,  in  the  column 
headed  Bafes,  and  take  the  firft  bafe  from  the  fecond, 
the  fecond  from  the  third,  Sec.  and  fet  the  remainders, 
refpe£Uvely,  in  faid  column  ;  each  of  which  will  be  the 
diftance  between  the  refpe&ive  perpendiculars.  Then 
add  the  firft  and  fecond  perpendiculars  together,  the  fe 
cond  and  third,  third  and  fourth,  &c.  and  fet  their  fums 
refpe&ively,  in  the  column  marked  Sum  of  Perpendicu^ 
ars.  Then  each  of  thefe  numbers,  multiplied  in  its  re- 
ipe&ive  bafe,  will  give  the  double  area  of  the  quadrilate 
ral  figure,  a»d  triangle,  (by  Problems  6  and  9,  pages  104 

and  107 

.X, 


°    F      O    F    F-S    E    T    S. 

Ex    A    M    PL    E       I. 

Let  A  £  C  D  E  F  G  H,  be  the  boundary  of  a  field,  by 
Nvhich  it  is  required  to  lay  off  a  field  containing  85 A.  3!*, 
"3,oP.  in  form  of  an  oblong,  by  aline  parallel  to  AI. 

A        13*90  Chains.          K 


fei 


\ 


'o\ 


I         J3 -90  Chains,       Ju 


O    F      O    F    F- S    E    T    S. 


No. 

Bafe. 
Ch. 

Perp. 
Ch. 

Safes. 

Sum  o 
Perpen 

Double 
Area. 

i 

0.00 

3.60 

6.20 

9.60 

59-52 

2 

6.20 

6.00 

2.80 

IO.OC 

28.00 

3 

9.00 

4.00 

( 

6.00 

6.50 

59.00 

4 

15.00 

2.50 

12.80 

7.80 

99.84 

5 

27.80 

5-3° 

2.70 

13.30 

35-91 

6 

30.5° 

8.00 

8.50 

15.00 

127.50 

7 

39.00 

7.00 

7.00 

7.00 

49.00 

'8 

46.00 

O.oo 

A.  21,9385 

4 


Area  21  A.  3R.  30?. 


40 


P.    30,160^ 


From"  85 A.  sR.  soP. 

Take  21        3  .    30  Area  of  the  off-lets^ 

-~       .    ^ 

Remains     63        3       30  To  be  laid  off* 
40)30 

4)3-75 
639.375  Square  Chains. 

By  Problem  4,  page  103,  divide  thus  : 
46)639.375(13.90  ch,  nearly,  from  A  and  I  to  K  and-I^ 


S. 


OF      OFF-SET 

EXAMPLE     2. 

Suppofe  a  meadow  bounded  on  a  brook,  as  under  fneci* 
feed,  the  area  of  which  is  required? 


I 
•S 


I 


O 

to 

•*-» 

C^ 

O 

H* 

S 


^.4  perches* 


V5  \r 


12.8  perches^ 


OF      O    F    F-S    E    T     S. 


157 


ToU>.  The  ift.  perpendicular  is  fet  oppofite  the  ill.  bate, 
becaufe  they  form  a  triangle*  . 

Meafured  in  Perches*. 


Sfo:'Bafe 

P. 

Bs 

S.P, 

DA 

i 

o.o 

0.0 

2.O 

5-° 

10.00 

2 

2.0 

5-° 

0.5 

9.0 

4.50 

3 

2-5 

4.0 

•5 

5.2 

7.80 

4 

4.0 

1.2 

.0 

2.4 

2.40 

5 

1.2 

•5 

2.6 

1.30 

<> 

5-5 

1.4 

•3 

6.5 

9-75 

8 

7.0 
8.0 

5-i 
5-4 

.0 
•5 

10.510.50 

10.716.05 

No. 

B. 

P. 

Bs 

S.P. 

DA 

9 

9-5 

5-3 

o.o 

7.5  oo.oo 

I 

o.o 

0.0 

1.4 

0.8 

i  .  i  i 

lo 

9-5 

•9 

3-4 

6.46 

2 

1.4 

o.S 

1.4 

1-7 

2.38 

II 

11.4 

1.2 

.6 

2.6 

4.16 

3 

2.tS 

0.9 

0.9 

0.27 

12 

13.0 

1.4 

.0 

6.4 

6.40 

4 

3-1 

o.o 

o.o 

o.o 

0.03 

T3 

14.0 

2.0 

10.  0 

20.CO 

t-3-77 

14 

16.0 

5.0(2.2 

9.2 

20.24 

15 

18.2 

4-2 

2-0 

5-3 

10.  60 

• 

1,88 

16 

20.2 

I.I 

1.3 

2.2 

3.96 

17 

22.0 

1.1 

I.O 

5.1 

5.10 

1  8 

23.0 

4.0 

2.0 

8.0 

16.00 

19 

25-0 

4.0 

I.O 

7.0 

7.00 

io 

26.0 

3-° 

0.3 

3-° 

0.90 

21 

26.3 

o.o 

5-7 

3.017.10 

4> 

32.0 

3'° 

1 

Note.  1 

"he  perpendicular  op- 

$>iso.2a 

polite  the  9th  Nation,  ex 

~ 

tends  to  the  extreme  point; 

jpo.i  i 
01.88 

and  that  oppofite  the  loth. 

to 

the  neareft  point.    The 

Area  of  the  ofF-fets.  91.99 

eff-fets  on  the  9th.  ftation 

oblong.  355.2. 

are  as  above. 

4,o)44,7  - 


p. 


3.A.  3R.  7?,  Anfvver. 


355-2 


158  OF      OFF-SET    S. 

EXAMPLE     3. 

With  ofF-fets  on  the  ad.  4th.  and  5th.  boundaries* 


No. 

Bearings. 

•  Diftan. 
uhuins 

N.  L. 

S.  L. 

E.D. 

W.  D, 

i 

N.  36  f  W 

30.00 

24.04 

!7-°5 

2 

N-56  JE 

21.60 

I2.O'.) 

I7.g6 

3 
4 

N.  26  J.  E. 

I3-44 

12.01 

6.00 

S.7iAE. 

18.96 

6.02 

17.98 

_^ 

5 

S.  26  ^E, 

13.46 

12.04 

6.60 

6 

S.  45  W. 

42.41 

29.99 

29.99 
47-84 

48.05   48.05 
Area  1152.20855  Square  chains* 

47.84 

O    F      OFF-SET 


159 


No. 

Bafe. 

'erpen. 

Bafes. 

Sum 
of  Perp. 

Doublt 

Area. 

I 

0.00  ' 

0.00. 

6.10 

3.  io 

18.9100 

2 

6.  io 

3.10 

4.05 

5-45 

22.0725 

3 

10.15 

2.35 

3-93 

5-21 

20.4753 

4 

14.01 

2.86 

5.12 

5.06 

25.9072 

5 

19.20 

2.20 

2.40 

2.20 

5.2800 

6 

21.60 

0.00 

0.00 

O.OO 

o.OOOO 

-w 

li 


i 


r 


I 

0.00 

0.00 

4-20 

2.10 

b.8200 

2 

4.20 

2.10 

3-85 

3-40 

13.0900 

3 

8.05 

I.30 

7.10 

3-*5; 

23.0750 

4 

i5'*5 

i*95 

3.8i 

I-95 

7-4295 

5: 

18.961  o.oo 

o.oo 

0.00 

0.0000 

1 

0.00 

o.oo 

5-1- 

2.05 

10.4900 

3 

5.12 

2.05 

4.88 

3-30: 

16.1040 

3 

IO.OC 

1.25 

3.46 

1.25 

4.3*50 

4 

13-4- 

o.oo 

0.00 

o.oo 

O.OOOO 

Area  of  the  off-fets,         87.99225  5  Q 

Map,  1152.20855 

A.  124,020080 

4 

,080320 

40 

1 24 A.  oR,  3.2i2booP.An* 


166  OF      OFF-SETS. 

EXAMPLE     4. 

Suppofe  a  water-courfe  to  be  the  line  between  the  land* 
of  A  and  B,  asunder  fpecined;  which  they  agree  to  ftrai- 
ten  by  a  line  from  the  point  C  to  D.  Query,  which  muft 
pay  the  other,  and  for  how  much  land  I 

C 


OF      OFF-SETS, 


OfF-fets  on  B  to  A.                 Off-fets  on  A  to  B* 

IN 

Bafe 

Pr.B's 

SP 

D.  A. 

N 

Bafe 

Pr. 

B»s 

SP 

D.  Av 

i 

0.00 

o.oo 

1.86 

4.14 

77004 

i 

o.oo 

o.oo 

2,00 

3-85 

7.7000 

2 

1.86 

4.142.58 

6.52 

16.8216 

2 

2.00 

3.85 

o.5o 

6.81 

3.4050 

3 

4 

4-44 
6.U 

2.38 

2.86 

bs  b\ 

M  -4 

5-24 
7.86 

8.7508 
12.6546 

3 

4 

2.50 
4.48 

2.96 
3-S4 

1.98 

1.46 

6.20 

6.56 

12.2760 

5 

7.72 

5.00 

1.58.8.70 

13.7460 

5 

5-94 

3-32 

1.34 

3.32 

4-4488 

6 

9-3° 

3-7° 

1.103.70 

4.0700 

6 

7.28 

^7 

10.40 

1 

i 

o.oo 

o.oo 

°-57 

5-7° 

3.2490 

i 

0,00 

0.87 

0.00 

3-79 

0.82 
1.98 

3-79 
6-55 

3.1078 
12.9690 

2 

3 

°-57 

5.70 

6.33 

1.16 
r.87 

12.03 
14.63 

13.9548 
27.3581: 

3 

2.8c 

2.76 

3-25 

7.56 

24.5700 

4 

3.60:8.30 

1.67 

15.12 

25.2504 

5 

6.05 

4.80 

3-95 

7.18 

28.3610 

5 

5-27 

6.82 

2-93 

10.20 

29.88601 

5 

IO.OC 

2.38 

2.82 

6.19 

17.4558 

6 

8.20 

1.  00 

5.98 

5.9800 

6 

12.82 

3.81 

3-78 

14.4018 

7 

Q.20 

I'.lo 

2.41 

6.22 

14.9902 

$ 

16.60 

8jii.6i 

3-62 

2.84    3.62 

10.2808 

%)  164.6088 

9  14-45 

i 

. 

. 

i 

o.oc 

0.00(2.50 

4-13 

10.32501 

82.3044 

2 

2.50 

4.13 

2.91 

6.91 

20.1081 

J 

5-41 

2.78 

7.98 

25.1370 

4 

8.56 

5.20 

3-3° 

7.67 

25.3110 

5 

11.86 

2.47 

4-34 

6-37 

27.645$ 

6 

16.20 

3-9c 

5.03 

3-9° 

19.6170 

7 

21.23 

•^296.5006 

148.250-5 

82.3044 

A.  6,59459 
4 

R,  2,37836 
40 

R-  15^3440?, 


.  B  mufl  pay  A  for  6 A.  ^R.  15,1344?, 

Note.  The  meafures  are  taken  in  chains  and  links 


DIVISION  OF  LAND. 


PR  O  B  L  EM    I. 

"X0  cut  off  from  a  Triangle  any  Part  thereof,  *  by  e 
Line  issuing  from  an  angular  Point  to  the  oppo-sit? 
Side  of  the  Triangle. 

RULE. 

As  the  area"  of  the  triangle, 

Is  to  the  fide  the  divifion  is  to  fall  on ; 

So  is  the  part  to  be  cut  off, 

To  its  proportion  of  that  fide. 

E    X    A    M    JP    L    E. 

Admit  the  triangle  ABC,  to  contain  650  fquare  per 
ches,  and  290  of  them  is  required  to  be  cut  off  towards 
A,  by  a  line  iffuing  from  the  point  C,  on  to  the  line  AB, 
which  is  40  perches  long. 

Sq.  Pr.      Pr.      Sq.  Pr. 
As  650    .  .  40  :  :  290  .  .  17.84  perches  from  A  to  B. 


DIVISION    OF    L  A  N  t». .         iCi^ 

PROBLEM    II. 

7^  ***/*    off  from  a    Triangle,  any  Part,  thereof,  i>y  & 
Line  running  parallel  to  one  of  it's  Sides* 

R    U    L    E. 

As  the  area  of  the.  triangle, 

Is  to  the  fquare  of  one  fide  the  diviflon  line  is  to  be  on  j, 

So  is  the  area  of  the  part  to  be  taken  off, 

To  the  fquare  of  its  proportion  of  that  fide  : 

The  fquare  root  of  which,  will  be  the  length  required,' 

EXAMPLE. 

Suppofe  the  triangle  ABC  to  contain  500  fquare  per 
ches,  and  it  is  required  to  cut  off  120  towards  A,  by  a 
line  parallel  to  BC  j  the  line  AB  bein^  40  perches 
and  AC  36* 


40  X  40  =  1600,  fquare  of  AB» 


As  500  .  .  1600  :  :  1210  .  .  -y/S^  •=  J9-^  Dearly,  the^^ 
diftance  from  A 


DIVISION    Of    L  A  &  D- 


^,  f  AB  .  ..  AG  ::  AC  ..  AD. 

1  40  . .    19.6  :  :  36  ..  17.64  Perches. 

PROBLEM     III. 

To  cut  off,  from  a  Triangle,  any    Part   thereof,    by  d 
Line  issuing  from  a  given  Point  in  one  of  it's  Sides', 

EXAMPLE. 

In  the  annexed  triangle,  containing  800  fquare  perched 
AB  is  50  perches  long,  and  AC  40,  and  it  is  required  to 
cut  off  towards  A,  500  fquare  perches,  by  a  line  ifluing 
from  the  point  F,  36  perches  from  A. 


RULE. 

By  Problem  i,  cut  off  500  fquare  perches,  by  a  line 
from  B  to  E. 

AC  AE 

Thus:  As  800  ,-.  40  :  :  5.00  .  .  25. 


AF          AB         AE 

Again,    As   36    .  .   50    ;  ;   25 


AO 


DIVISION    OF    LAND. 


PROBLEM     IV. 

To  cut  off,  from  a  Square,  or  Oblong,  any  Part  thereof* 

Let  ABCD  be  a  fquare,  each  fide  whereof  is  2,0  chains, 
and  it  be  required  to  cut  off,  toward  AB,  160  fquare 
chains,  by  a  line  parallel  to  AB. 

Note.  By  Problem  4,  page  103,  lay  off  the  propofe 
tity,  thus : 

AB         AEorBF. 
•  2o)i6o(  8.0  Chains* 


D 


The  method  of  diving  land,  in  other  forms,  will  be 
{hewn  in  examples  as  they  occur. 

EXAMPLE     i. 
Taken  in  Perches. 

A  Field,  bounded  as  under  fpecified,  is  to  be  divided 
into  two  equal  parts,  by  aline  parallel  to  AD  or  BC.  Re 
quired  the  diftance  from  AB,  that  the  divifionline  EFmuft 
runi 


DIVISION    OF    LAN  D; 


Stations. 

Bearings. 

Dift.  Per. 

N.  L. 

S.  L. 

E.  D. 

W.D, 

AB 

South. 

29.6 

29-6 

BC 

N.  80°  \\ 

60.0 

10.4 

59-i 

CD 

N.39iW 

45-5 

34-7 

38.6 

DA 

S.  80  E. 

89.4 

J5-5 

87.:, 

45-  * 

45-1 

87.7 

87^ 

Area  of  the  Map  ABCDA  2174.62;  fquare  perches, 

i 

\  to  be  taken  off  1087.31  fquare  perches. 

Note.  The  learner  is  requefted  t>o  work  all  the  operate 
ons  in  full,  in  this  and  the  following  examples. 


DIVISION    OF    LAND.          167 

Continue  AB  and  DC,  until  they  inter  fe£t  at  G  ;  then 
tn  the  triangle  CBG,  are  given  the  fide  CB  60  perches, 
and  by  the  bearings  of  the  lines,  all  the  angles,  viz.  CBG 
100°,  CGB  39°  30',  GCB  40°  30-',  to  find  the  other  re- 
<mifites  ;  and  by  Cafe  i,  Oblique  angled  Trigonometry, 
page  80,  the  fide  BG  is  found  to  be  6 1.26 perches;  then 
by  Problem  10,  page  108,  find  the  area  of  the  triangle 
CBG. 

As  radius  90°  10.00000 

IstoCBl  60  1.77815 

BGJ  61.26  1.78718 

So  is  fine  angle  B  100°  9-99335 

13.55868 

10.00000 
t~\  - 

"To  the  double  area  3619.8  3-55868 

Area  of  CBG  1809.9  fquare  perches. 

Add  1087.31  SB  \  the  area  of  the  map. 

Area  of  EFG  =  3897.21 
Then  to  find  GF,  by  Problem  2,  page  163. 

CGB  fqr.BG          FGF  2fqr.ofFG 

As  1802.9     ..     3753     ::     2897.21     ..     ^6007.64= 

GF. 

77.51  perches,  nearly. 

Then  \  GF  —   GB   =  BF 

177.51 — 61.26  =  16.25  perches,    ^e   anfwer. 

Draw  FE  parallel  to  BC,  and  it  is  done  as  required. 

By  the  application  of  this  method,  a  tratl  of  land  may 
fce  divided  accurately,  in  any  proportion,  by  a  line  run- 


i53 


DIVISION    OF    LAND, 


rung  in  any  afiigned  direction,  where  the  triangle,  formed 
by  continuing  the  lines,  until  they  interfeft  (as  the 
preceding)  is  not  large ;  but  in  pra&ical  operations,  it 
frequently  happens,  that  th  e  logarithm  of  the  double  area, 
is  more  than  a  number  can  be  found  for  in  the  tables  in 
common  life,  without  taking  proportionals,  which  is  trou~ 
blefome,  and  uncertain  to  be  true  ;  as  is  the  cafe  in  the 
prefent  inftance.  Therefore,  in  order  to  give  a  clear  rule, 
invariably  true  in  all  cafes,  I  bring  forward  the  preced* 
ing  triangle. 


Always  find  the  longeft  fide  oF  the  triangle,  for  a  bale* 
as  by  Cafe  I,  Oblique  Angled  Trigonometry,  page  80, 
CG  is  found  to  be  92.89  perches  ;  then  let  fall  a  perpend^ 
cular  thereon  from  the  oppofite  angular  point,  as  BIj 


DIVISION  OF  LAND.       169 
fa 

again,  by  Cafe  i,  Right  Angled  Trigonometry,  page  68, 
this  perpendicular  is  found  to  be  38.97  perches,  and  being 
multiplied  into  the ibafe,  gives  3619.9  fquare  perches,  the 
double  area  of  the  triangle,  the  fame  as  before  nearly,  and 
the  fmall  difference  is  owing  to  the  logarithm  being  larger 
than  a  number  could  be  found  for  in  the  table  :  this  being 
done,  proceed  to  find  the  place  of  the  <}ivifion  line,  as  be 
fore  taught.  Or, 


.  When  the  three  iides  of  an  oblique  angled  triangle  are 
iw  hud  the  ar^o,  tin*  hafee  made  by  the  perpendicular, 
as  above,  may  be  found  by  the  rule  to  Cafe  6,  Oblique  An, 
gled  Trigonometry,  performing  the  operation  either  by  the 
logarithms,  or  arithmetically  ;  then  find  the  perpendicalar,  by 
the  Note  to  Problem  1 3,  page  28  ;  and  thence,  the  area,  more 
concife  and  true,  than  taught  in  Gibfon's  Surveying. 

r  CG        Diff.  of  CB  &  BG      C3  &  BG 

As<  92.89     ..         1.26         ::         121.26     ..   1.64  Diff.  of 
I         CI  and  IG. 

Then  from  f  CG  =  46.44,  take  ~  the  difference  .82,  leave's 
45.62  CL 

Again,  the  fquare  of  CI  is  2081.1844.  The  fquare  of  CB  is^ 
3600,  Their  difference  is  1518.8156 ;  the  fquare  root  of  which 
is  38.97  BI,  the  fame  as  before. 

I  {hall  here  give  another  method  to  make  a  Map  from 
the  Field  Notes,  which  will  be  found  very  eafy  and  con 
venient  in  many  inftances,  although  pra&ifed  by  none  that 
I  know  of, 


K  U  L  E. 


DIVISION    OF    LAND, 
RULE. 

Draw  a  meridian,  and  on  It  defcribe  a  circle  with  the 
chord  of  60°  in  the  campafles ;  then  take  in  the  compafles 
from  the  fame  line  of  chords,  the  feveral  bearings,  and  lay 
them  on  the  circle  from  f aid  meridian,  the  northerly  from 
the  top,  and  the  foutherly  from  the  bottom,  and  number 
them  i,  2,  3,  4,  &c.  as  in  the  annexed  example ;  then 
from  the  centre  (which  will  always  be  the  place  of  begin" 
ning)  through  No.  i,  rlraw  a  line,  on  which  lay  the  firft 
diftance  ;  then  lay  a  parallel  ruler  on  tbe  centre,  «nd  No. 
3,  and  open  it  to  the  fecond  itation,  and  there  draw  a  line, 
and  lay  off  the  fecond  diftance,  and  fo  proceed  with  every 
number,  remembering  to  draw  the  line  northerly  or  fouth 
erly,  as  indicated  by  the  bearing,  arid  if  the  laft  three 
points  be  in  a  range,  it  denotes  the  work  to  be  true. 


AB  &3J«i*1 

BC  N  45  W 
CD  N  15  £E 
BE  S  77  E 
EF  S  87  i.  E 
FG  S  60  E 
GH  South 
HA  N  85  W 


Ch. 

13.18 

5.40 
8.00 

i°-75 
7.40 

14. 60^ 


•Field  Notes^ 


(See  the  following  Figure*) 


DIVISION    OF    LAND. 


EXAMPLE     2. 

Required  the  area  of  the  preceding  Map,  and  to  cut 
off  loA.  3R.  24?.  to  the  weftward,  by  a  line  iffuingfrom 
the  point  A,  and  to  find  the  bearing  and  diflance  of  the 
divifion  line. 


Stations. 


i&C 


CD 


"EF 
FG 


Bearings.  Dift.  CH. 


5,60 


N.  L. 


N  45  W 


8,6  1 


5^40 


S  77  E  j      8,00 


to  E 


7,40 


5,20 


0,47 


S.  L. 


E.  D. 


4-57 


1.80 


3-7° 


£,44 
7,80 


6,41 


W.D. 


3.23 
8,61 


W 
HA 


South. 


5.4B 


14,60 


14.54 


Area  2rA.  iR,  35?, 


36,38 


DIVISION    OF    L  A  NIX 
C  I  F 


Find  t,he  area    of  ABCDEA,  iuppofing  that   to   be 
neareft  the  quantity  propofed. 


Stations. 

Bearings,  i  Diflan. 

N.L. 

S.  L. 

E,D 

WD 

AB 

S35iW 

5.60 

4-57 

3-23 

BC 

N45  W 

12.18 

8.61 

8.61 

CD 

NiSiE 

5.40 

5.20 

1.44 
7-8^ 

"   i  i        mm*   i 

DE 

S  77  E 

8.00 

i.  80 

EA 

S     E 

7-44 

2.6c 

£rea  9A.  iR.  23? ioA.  sR.  24?-  =*  iA.  aR 

IP.  =  i.5o625A.  to  be  taken  out  of  the  triangle  AEFA 

Find  the  area  of  AEFA. 


Stations,  i 

Bearings. 

Diftan. 

N.L. 

S.L. 

E.  D. 

W.D. 

AE 

N     W 

7.44 

2.60 

EF 

N  87}  E 

i°-75 

0.47 

10.73 

FA 

S      W 

7.91 

8.i3 

DIVISION    OF    LAND,  173 

Area  4.05  acres. 
Then,  by  Problem  I,  page    162. 

fAFFA          FF     •  •  AFTA          FT     ") 
As4  J     '^A  '•  L  Chains. 

t     4-05    ..    10.75  ::  1.50625  ..   3.99  J 

To  find  the  bearing  and  diftance  of  the  ctivifion  line  AI 
or  IA. 


Stations 

Bearings. 

Dift. 

N.L. 

S.  L. 

E.D. 

WD 

2.60 

AE 

as  before. 

7-44 

El 

INF37   |E 

3-99 

0.17 

3-99 

'•39 

IA 

s   w 

7.61 

With  the  difference  of  latitude  7.61  chains  fouth,  and 
departure  1.39  chains  weft;  the  bearing  and  diftance  of 
the  divifion  line  is  found  to  be,  viz. 


flA  S  o°    10'  W")  0 
.    |AINy9oI(/E   j  8.7*  chains 


EXAMPLE     j. 

Taken  in  Perches. 

Let  ABGDEFGHIA  be  a  trad  of  land,  to  be  divided 
into  two  equal  parts,  by  by  a  line  from  the  point  I.  Re 
quired  the  bearing  and  diftance  of  the  divifion  line. 

Again  ;  it  is  required  to  cut  off  38  acres,  16  A  perches 
to  the  fouth  end  of  this  traft,  by  a  line  running  from  i*. 


I)  I  V  I  S  I  O  N    O  F    LAN  D; 


due  Weft,  40  perches,  to  a  well.  The  bearing  and  dl, 
ftance  of  the  divifion  line,  from  the  well  to  tjie  oppofite 
Boundary,  is  required. 

t  The  field  notes  are  as  under. 


0\ 


ON 


W 


CO 


w 


CO 


co 
u 

VJ 

H 


CO 

VJT 

-s> 

w 


VO 
O 


Station 


td 


o\ 
r 

U) 


CN 


Oi 

CO 


01 


B. 


CO 
CO 


CO 


CO 

VI 


W 

b 


s 


(See  the  following  figure,} 


DIVISION    O  F    L  A  N  D.        175 


B 


Find  the  area  of  IABCI. 


Stati. 

Bearings. 

Dift. 

N.L. 

S.  L. 

E.  D. 

W.D. 

IA 

N6a°JW 

59- 

27-5 

52.3 

AB 

N  19  E 

108. 

I02.I 

35-2 

BC 

S77E 

91. 

20.5 

88.7 

CI 

s  w 

109.1 

71-7 

Area  8722,3  perches. 

176        DIVISION    OF    L  A  N  15. 

From  half  the  area  of  the  map,   12192.9  perches 
Take  the  above  area,  8722.3  perches 


Leaves  lefs  than  hair 
Find  the  area  of  ICDI. 


3470.6 


Stati. 

Bearings. 

Dift. 

N.  L. 

S.  L, 

E.D. 

W.D. 

1C 

N     E 

109.1 

71.7 

CD 

S  27  E 

TI5- 

102.5   53'2 

DI 

S     W              | 

6.6 

123.9 

Area  652,2.1 

ICDI    .  .    CD  :  :    ICNI    .  .    CN 

6522.1  .  .    115    :  :  3470, 


«  .  .   CN   I 

D.6  .  »  61.193 


Perches. 


To  find  the  bearing  and  diftance  of  the  diviiion  line  NI 
or  IN. 


Sta. 

Bearings. 

Dift. 

N.  L. 

S.L. 

E.D. 

WD 

1C 

as  before. 

109.1 

71.7 

CN 

S  27°  E 

61.2 

54-5 

27.8 

99-5 

NI 

S     W 

54-6 

'  With  the  difference  of  latitude  54-6  fouth,  and  depar 
ture  99.5  perches  weft  j  the  bearing  and  diftance  is  found 


to  run,  viz. 


This  completes  the  firft  divifion,  as  required. 


DIVISION    OF    L  A  N  Da 
For  the  fouthern  dlviiion. 
find  the  area  of 


Stati 

Bearings. 

D.P. 

NLf 

S.L. 

E.D/WD 

OE 

Eaft. 

40 

40.0! 

EF 

S  15-  J  E 

76 

73-2 

2O.3 

FG 

Weil, 

70.9 

1 

70.9 

GH 

N36  VV 

47- 

3^.0 

J27.6 

HO  |     N    E     I        rj5.il         38.2) 
Area  5270.5  Perches. 

From  38 A,  oR.   16.5?.  =  6096.5?. 
Take  the  above  area  %        5-70.5 


Leaves 
'Find  the  area  of 


82,6.  Per. 


Statij  Bearings. 

Dift. 

NL 

S.L. 

£  r 

WD 

3-^ 

OH 

S     \V 

35-^ 

HI 

North. 

64.3 

64.3 



I0|    &      E 

2,9.1130.2 

Area  i  3218, 13  Perches. 

H0IH  .  .  Ill  :  :  H0VH  .  .  HV 

338. 13  .  .  64.3    :  :    82,6  .  .  43.2,4  Perches, 


A  a 


3         DIVISION    OF    LAND. 

.Find  the  bearing  and  diftance  from  the  Well  to  V. 


Stati1 

Bearings. 

Dift.NL 

3.L.1E.D. 

WD 

OH 

as  before. 

35-* 

33.a 

HV 

North. 

43-3.43-2 

V0 

S     E 

8.0 

38.2 

With  the  difference  of  latitude  and  departure  of  V0, 
the  bearing  and  diftance  of  the  divifioii  line  from  the  Well 
to  the  oppofite  boundary,  is  found  to  run,  viz. 


Which  completes  the  divifioh  as  required. 
E  X  A  M  P  L  E.       4. 

Admit  a  field  bounded,  as  under  fpeci!iedt  is  to  be  di 
vided  into  three  equal  parts,  fo  that  each  may  have  the 
benefit  of  a  well  therein,  and  which  bears  from  the  place 
of  beginning  A,  N.  60°,  W.  14.35  chains,  and  is  to  be 
the  firft  divifion  line.  The  quantity  in  each  part,  the  bear 
ing  and  diftance  of  the  other  divifion  lines  are  demanded:, 


Stati 

Bearings. 

D.     C. 

N.    L.1 

S.     L 

E.  D. 

W.  D. 

AB 

S  80°  W 

i9-5i 

3-39 

19.21 

EC 

N  36   iW 

16.61 

I3-39 

9.82 

CD 

N  70  E 

18.90 

6.46 

17.76 

. 

DE 

S  63  i  E 

12.62 

5.68 

11.27 

EA 

South. 

10.7^ 

10.78 

I 

Area.3SA.  311.  17?.  «-5- 3*=  i2A.  3R.  32?. 


BIVISION    OF     LAND, 

D 
R 


179 


Find  the  area  of  QABQ- 


Stations. 

Bearings. 

Diftan. 

M.     L. 

3.L. 

E.  D. 

W.   D. 

OA 

S    60°    E 

i4-35 

7.17 

12.42 

AB 

S  So  W 

19.51 

3-39 

19.21 

B0 

N      E 

1 

10-56 

6.79 

Area  8.99  acres. 

From  one  third  of  the  map,  viz.  12.95  acres. 
TakeQABQ  8.99 


Leaves 


Find  the  area  o 


Stations 

Bearings. 

Dift. 

isr.L. 

3.  L. 

E.  D. 

W  D 

QB 

S    W 

10,56 

16,61, 

6.79 

BC 

Ns6^W 

16.61 

'3-3? 

9.82 

Co 

S      E 

^.83 

Area  9.7 3  acres, 


480         DIVISION    OF     LAN  p. 

GBC0    .  .    BC  :  :  BP0B  .  .  BP 
9.73     .  .    16.61   :  :  3.96    .  .  6.76 

To  find  the  bearing  and  dittance  of  FQ  or  0P, 


Stati. 

Bearings. 

Bift. 

N.L. 

3.   L.tE.  D. 

I 

W.D; 

OB 

as  before. 

io.fr6i 

! 

6.79 

BP 

.V  36  4  W 

6.76 

5-45 

| 

4.00 

P0 

N     E 

5-II 

|I0.79 

With  the  difference  of  latitude  and  departure  for 
is  found  for  the  anfwer. 


runs 


Anfw.    V-Si  luli&  ^  ^4°  39w  (  1 1.93  chains, 
ij.  -  04  ^9        «* 

9-73 
Leaves  T0CP  'r=  5.77' 


Trora 

Take  BP 013 


From  I  of  the  map  =  12.95 
iTake?0GP  =  5,77 

Leaves  C0RC  =  7.18  acres. 

Find  the  area  of  0CD0. 


Sta. 

[Bearings. 

Diitan. 

N.L. 

S.LJE.    D 

W.  D. 

0C 

N.-    W. 

:>.83 

16.61 

CD 
1)0 

7    70  h 

18*90 

6.46 

17.76 

S     W 

9.39 

' 

1.15 

Area  7.9  acres, 


DIVISION    OF    LAND, 


181 


c  0CD0  .  .  CD  :  :  CQRC  .  .   CR 
I      7.9     .  .     18.9    ::     7.18  .  .   17.17 

To  find  the  bearing  and  diftance  of  RQ  or  0R. 


Station 

Bearings. 

Diftan 

N  T 

S  I 

E.    D.  W.  D. 

oc 

as  before. 

*.!>: 

i   16.61 

CR 

N  70  E 

I7*1/ 

S-&1 

16.13 

Ro 

S      W 

0.70, 

0.48 

As  difference  of  latitude 


Is  to  radius 
So  is  departure 


96' 


8,70 
,48  — 


10.00000 

9.68124 
9.68124 


To  tangent  bearing  3°  9' 

I  have  let  down  the  above  ftatement,  as  the  departure 
is  a  negative  number.     See  page  55 

The  diftance  being  found,  as  before,  we  have 


*    r        CRO  runs  S  o°  c/  Vvr  ?  0 
An^-    i  OR  runs  N  3     cJK    ^  ^ 

EXAMPLE     5. 

Admit  apiece,  pf  land,  bounded  as  under  fpecified,  is  to 
be  divided  thus,  viz.  by  a  line  GI  parallel  to  AB,  to  iffue 
!rom  the  point  G,  in  the  line  BC  5.45  chains  from  the  ccr- 
ler  3,  and  on  the  line  BG  to  lay  off  two  acres  in  a  paral- 
t  llogran,  and  cr.lciJate  the  remainder  cut -cfT  by 'this  divi- 
.on  line  GI. 


j8*        DIVISION    OF    LAND. 

Again  •  a  divifion  line  to  iflue  from  the  point  E,  to  the 
oppofite  boundary  BC,  and  to  run  parallel  to  AB,  and  ano* 
ther  diviiion  line  to  iffue  from  the  point  H,  in  the  line  CD 
4.16  chains,  from  the  corner  C,  and  to  run  parallel  to  CB, 
until  it  interfe&s  the  former  divifion  line.  Required  the 
area  of  each  piece  feparately. 

The  field  notes. 

Ch. 

AB  N  63°  W  5.56 
BC  N  27  E  18.56 
CD  S  27  E  10.81 
.DE  S  6a£  W  4.05 
EF  S  51  W  5.00 
FA  590i8'W5.03 

C 


o 


DIVISION    OF    LAND. 


it. 


The  Map  being  made,  draw  GI  as  propofed,  and  on 
BG  lay  off  two  acres,  by  the  pai^allel  line  RS,  which  by 
Problem  4,  page  103,  will  be  found  to  be  3.67  chains  near- 
,ly  from  the  line  BG  ;  then, 

AB~  BR  =     Mi 

5.56  — 3.67  =—  1.89  Chains. 

Now,  to  find  the  diftances  SI  and  IF,  find  the  "bearing 
and  diftance  of  SF. 

W.D, 


Stations. 

Bearings. 

diftance. 
5-°3 

N.  L. 

S.  L. 

E.  D. 

FA 

S  59-18'  VI 

a-57 

AR 

N.  63°  W. 

1.89 

5-45 

0.85) 

RS 

N.  27   E 

4.85 

24/ 

SF 

S.        E. 

3-i3\  3*54 

4-33 


With,  the  difference  of  latitude  and  departure,  SF  is 
found  to  bear  S  48°  31',  E  4.72  chains  ;  then  in  the  tri- 
-angle  SFI,  are  given  the  angles  by  the  bearing  of  the  IHH&, 
viz,  FSI  14°  29',  SFI  53°  46;,  SIF  111°  45 /,  and  the 
fide  SF  4.72  chains,  to  find  the  fides  SI  and  IF  ;  and  by 
Cafe  i,  Oblique  Angled  Trigonometry,  they  are  found  to 
be  SI  4.10  chains,  IF  1.27  chains;  then  to  find  the  a 
of  ARSIFA,  are  the  following  field  notes. 

SI  +  GS  «  GI 
4.10  -f  3.67  =  7.77  Chains. 

Ch. 

N  63°  W     1.89-1 
N  27     E      5.45  j 

S  63     E     4.10  ^AreaiA,  711,  •&<• 
S  5iW     1.27  ] 
S  59.18  W5.o3J 
Now  IF  —  KF  =  El 


AR 

RS 

SI 

IF 

FA 


184          DIVISION    OF    LAN  IX 

From  the  point  E,  let  fall  a  perpendicular  on  the  line 
GI;  then  in  the  right  angled  triangle  VEI,  are  given  the 
hypothenufe  3  chains,  73  links  ;  and  by  the  bearings  of 
the  lines,  the  angle  VEI  21°  45',  VIE  68^  15',  to  find  the 
bafe  VI,  i  chain,  38  links,  and  perpendicular  VE  3  chains 
46  links  =  GO. 

GI  —  VI  ^  GV  =,  OE 
7-77  —  *-38  —  6-39  —  6-39  chains. 

To  find  the  area  of  IGOEI,  the  following  notes  ariio 
from  the  preceding  operations,  vis. 

Ch. 
IG     N  63°  W  7.77- 

,rea  z A.   iR.  33!  P,  -f 


ILr  JN    03V     VV    7-77^ 

GO  N  26     E    3.46  /   . 

OE  S    63     E    6.39  fAr{ 

El  S   5i    W3.73J 


BG  +  GO  =   BO 

5«45  +  3-46  =  8.91  chains* 

And  BG  —   BO  =  OG 

18.56  —  8.91  =9.65  chains. 

From  the  point  H,  let  fall  a  perpendicular  on  the  line 
OC  ;  then  in  the  right  angled  triangle  HNC,  are  given 
the  hypothenufe  4  chains,  j 6  links,  and  by  the  bearings 
of  the  lines,  the  angle  NCR  54°,  and  NHC  36°,  to  find 
the  bafe  NC,  2,  chains,  44  links,  and  perpendicular  N.H^ 

LO,  3  chains,  37  links. 

Then  OC  —  NC  =  ON   =  HL 

9.65  —  2.44  =  7-2H  =•  7.211  chains. 


DIVISION    OF    LAND.  185 

To  find  the  area  of  LOCHL,  the  following  notes  arife. 

Ch. 

LO     N  63°  W  3.37^1 
OC     N  37     E   9.65     , 

CH     S   27     E    4  16  r*Area  aA'  3R-  X3'6* Perch* 
HL    S    27    Wy.aiJ 

EO  —  LO  a-  EL 
^•39  —  3-37  s=  3-02  chains. 

CD  —  CH  =  HD 

10.81— 4. 1 6-=  6.65  chains. 

To  find  the  area  of  ELHDE,  the  following  notes  arife 

Ch. 

EL      N  <53°  W  3.o:T| 
LH     N  27     E  7.21  I   . 
HD     S    ^     E  6.65  ,^Area  *A*  IR« 
DE     S   6 


EXAMPLE    6. 

Suppofe  a  furvey  to  be  made  as  follows,  viz. 

AB  eaft  20.  chains, 

BC  north  18.  chains, 

CD  north  30°  weft,  fo  far  as  will  inclofe  120  £  acres, 
the  north  boundary  DE,  to  be  due  weft  17.  chains  from 
the  north  30°  weft  line.  Required  the  diftance  on  this 
line ;  alfo  the  bearing  and  diftance  of  the  clofmg  line  EA> 
to  include  iso-|  acres. 

Note.  The  propriety  of  this  example  being1  under  the  head  of 
Divifion,  may,  perhaps,  be  doubted  by  fome  ;  but  the  calcu 
lations  are  fo  nearly  allied  thereto,  that  J  thought  it 
We. 

B  b 


1 86 


DIVISION    OF    LAND. 


From  the  point  C,  clraw  Cd  due  weft  17  chains ;  then 
by  Problem  9,  page  107,  the  area  of  ABCdA,  is  found 
to  be  33.3  acres  ;  continue  AB,  and  from  the  point  C,  re- 
verfe  CD,  to  meet  AB  in  the  point  L  ;  then  in  the  right 
angled  triangle  BCL,  are  given  the  perpendicular  BC  18 
chains,  and  the  angles,  by  Pofition  4,  page  12,  and  Po- 
fition  2,  page  10,  to  find  the  bafe  T*L  10.39  chains?  and 
hypothenufe  CL  20.79  chains ;  then  by  Problem  6,  page 
13,  the  area  of  the  triangle  BCL,  is  found  to  be  9.35 


acres. 


ABCDEA  —  ABCdA  =  AdCDEA 
120.5       —      33.3      as       87.2  Acres. 

.    ,  f  ABCdA  +  BCLB  «  ALCdA 

i     33-3     +     9-35       «     42.65  Acres. 

Then  fay, 

f  ALCdA    . .   LC  :  :  AdCDEA  . .  CD 
LS  I  4^*65     .  .  20.79    : :     87.2    .  .  42.50  Chains 


'{See  the  following  Map.) 


DIVISION    OF    LAND.  187 

E  D 


Jb  10.39 


From  thence  the  following  notes,  to  prove  the  work, 
by  calculating  the  quantity  of  land  thereby  inclofed,  ar^d 
to  find  the  bearing  and  diftance  of  the  clofing  line  EA. 


Stati 

Bearing'  D.  C. 

N.L. 

S.  L 

E.  D.W.D. 

AB 
BC 

Eaft.   po  oo 
North.  18-00 

20.  oc 

f 

18.00 

CD  JN30WJ42  50 

36.80 

21.25 

DE 

Weft.  (17.00 

17.00 

EA 

S     E| 

54.80 

18.25 

With  the  difference  of  latitude  and  departure  of  the  clo 
line  EA,  it  is  found  to  run  S  18°  35',  £57  chains,  7^ 
links, 


O    F 


INTERSECTIONS. 


INTERSECTION  is  the  bearings  of  an  objeft  from 
two  ftations  j  the  bearing  and  diftance  of  the  ftations 
being  known,  the  diftance  to  the  obje&  may  be  found : 
thence  the  plan  of  a  field  may  be  taken  by  interfe&ions? 
•when  all  the  corners  thereof  can  be  feen  from  two  ftations, 
and  the  area  of  the  field  determined  by  calculations :  an 
example  of  which  follows  j  the  bearing  and  diftance  be 
tween  the  two  ftations,  and  the  bearings  from  them  to  the 
feveral  corners  of  the  field,  being  as  in  the  following  table. 


The  ftations  H  and  I,  North  and  South  28  chains. 


No. 


Bearings. 


HA 


HB 


HC 


HD 


HE 


HF 


HG 


S85f  E 


S  68  E 


S  40 


No. 


IA 


IB 


1C 


ID 


IE 


IF 


Bearings. 


N42  i  E 


S  82 


N73 


IG  |  N  60  E 


OF    INTERSECT!  p*  N  S.         189 

By  Cafe  i,  Oblique  Angled  Trigonometry,  find  the  di" 
ftance  from  either  ftation,  as  from  I,  to  the  feveral  cor 
ners  of  the  field,  thus  : 

To  find  IA. 

As  fine  [  A  70°  9.972199 

Is  to  IH  38  ch.  1.44716 

So  is  fine  |_  H  8iQ  30'  9.99520 

11.44^36 
9.97399 


To  IA  29.47  1-46937 


To  find  IB. 


As  fine  [  B 
Is  to  IH 

So  is  fine  [  H 

5* 
28 

85.45 

9-89653 
1.44716 
9.99880 

11.44596 
9.89653 

To  IB  35.43  1.54943 


(See  the  following  Map.) 


j9o       OF    L_N  T  E  R  S  E  C  T  I  O  N  S. 
THE     &    A    P. 


H 


To  find  ICL 


As  fine  [  C 
Is  to  IH 

60.30 

2S 

9-93970 

So  is  fine  1  H 

65 

9.96717 

11.41433. 

9,93970 

To  1C 


1.47463 


OF    INTERSECTIONS.        191 


TO  find  ID 

50.45 

As  find  [  D 
Is  to  IH 

So  is  fine  [  H 

50.45 
58.15 

'9.88896 

1.447*6 
.9.92960 

11.37676 
9.88896 

To  ID  30.75  1.4978© 


To  find  IE. 

As  fine  [  E 
Is  to  IH 

47              9.86413 

38                       1.447*6 

So  is  fine  |_  H 

35-3°            9-76395 

ii.  aim 
9.86413 

To  IE  22.23  1.34698 


To  find  IF. 

As  fine  [   F  78  9.9904® 

IstoIH  38.  1.44716 

So  is  fine  [  H  38.30  9.67866 


9.99040 
To  IF  33-6<s 


OF    INTERSECTIONS, 

To  find  10. 


As  fine  [  G 
Is  to  IH 
So  is  fine  [  H 

80 
28 

40 

9-99335 
1.44716 
9.80807 

11.25523 
9-99335 

ToIG 


18.27 


1.26188 


The  bearing  and  diftance  from  the  ftation  I,  to  each 
corner  of  the  field,  being  afcertained,  find  the  difference  of 
latitude  and  departure  of  each  line  inclofing  the^field ;  and 
A  being  the  corner  of  the  furvey  to  begin  with.  Reverfe 
the  line  from  the  next  fucceeding  corner  to  the  point  I,  &c^ 
as  follows. 

To  find  the  difference  of  latitude  and  departure  of  AB. 

WD 


StatijBearings. 

Dift. 

N.L.jS.  L. 

E.D. 

BI  S42°iW 

35-43 

26.12 

IA 

N28  JE 

29.47 

25.90 

0.22 

14.06 

AB 

N      E 

9.88 

23.94 


To  find  the  difference  of  latitude  and  departure  of  BC» 


Stat. 

~cT 

Bearings. 
S5iiW 

Dift. 
29.83 

N.L. 

S.  L. 

E.D. 

W  D 

23-35 

18.57 

IB 

N42|E 

35-43 

26.12 

23.94 

BG 

s    w 

7-55 

°-59 

OF    INTERSECTIONS.        195 

To  find  the  difference  of  latitude  and  departure  of  CD. 


Stati 

Bearings. 

Diftan. 

N.     L. 

S. 

DI 

571  W 

3°-75 

IO.O 

1C 

N5i.  £E 

29.83 

18.57 

CD 

S       E 

8-5 

E,     D. 

W.   D. 

29.08 

23-35 

5-73 

To  find  the  difference  of  latitude  and  departure  of  DE, 


Station. 

Bearings. 

Dift. 

N.  L. 

2.90 

El 

N82iW 

22.23 

ID 

N7i  E 

3°-75 

IO.OI 

DE 

S      W 

3.  L. 


E.  D.W  D 

[22.04 


29.08; 


12.91 


7.04 


To  find  the  difference  of  latitude  and  departure  of-EF. 


Station 

Bearings. 

Diftan. 

NL 

S.L. 

E.    D. 

W.  D. 

FI 

S73iW 

13.66 

3-88 

13.09 

IE 

S  82  A  E 

22.23 

2.90 

22.04 

EF 

N    W' 

6.78 

8-95 

To  find  the  difference  of  latitude  and  departure  o 


Stati 

Bearings. 

Dift. 

NL 

S.L. 

E.  D. 

W.  D. 

GI 

S6o  W 

18.27 

9-*3 

15.82 

IF 

N73JE 

13.66 

3-88 

13.09 

FG 

N    E 

5-^5 

*-73 

C  c 

i94        OF    INTERSECTIONS. 

To  find  the  difference  of  latitude  and  departure  of  GA. 


Sta. 

Bearings. 

Diftan. 

N.    L. 

S.    L. 

E.    D. 

W.  D. 

AI 

S  28  J  W 

29.47 

25.90 

14.06 

IG 

N    60  E 

18.27 

9-J3 

15.82 

GA 

N.     W. 

16.77 

1.76 

This  being  done,  proceed  to  bring  into  a  traverfe  table, 
the  difference  of  latitude  and  departure  of  the  feveral 
boundary  lines,  viz.  AB,  BC,  &c.  In  the  column  for 
bearings,  put  the  letters  to  denote  the  bearing  of  each 
line,  and  leave  a  blank  for  the  degrees  ;  alfo  the  diftance 
column  leave  blank. 

THE    TRAVERSE   TABLE. 


Stati 

Bearings. 

D.    C. 

N.    L. 

S.     L. 

E.  D.  W.  D. 

AB 

N88°44'E 

9.88 

0.22 

9.88| 

BC 

S    4.28  W 

7-57 

7-55 

|     °-59 

CD 

S  33,48  E 

10.30 

8.56 

5-73 

DE 

S  2,8.37  W 

14.71 

12.91 

1    7.04 

EF 

N  52.51  W 

11.22 

6.78 

,     8.95 

FG 

N  27.28  E 

5.92 

5-*5 

2-73 

GA 

N.  5.59  W 

16.86 

16.77 

i     1-76 

!  29.02 

29.02 

18.34    18.34 

,   .AreaaSA.  iR.  nP.  + 


OF    INTERSECTIONS.         195 

With  the  difference  of  latitude  and  departure  of  AB, 
find  the  bearing  and  diftance,  thus  : 

To  find  the  bearing* 

As  departure  9.88  0.99476 

Is  to  radius  90  10.00000 

So  is  difference  of  latitude       0.22 —   9.34242; 

9-3424* 
0.99476 

To  co-tangent  bearing         88°  44'       8.34766 


To  find  the  diftance. 

As  radius                          90^  10.00000 

Is  to  departure                 9.88  0.99476 

So  is  co-fecant  bearing         88°  44'     10.00011 


10.99487 

10.00000 


To  the  diftance  9.^8  0.99487 


To  find  the  bearing  of  BC» 

As  difference  of  latitude         7.55.        0.87795 
Is  to  radius  90°  10.00000 

So  is  departure  0.59  —      9.77085 

9.77085 
0.87795 

To  tangent  bearing  4°  a3'        8.89290 


196      OF  INTERSECTIONS, 

To  find  the  diftance. 

As  radius  90°  10.00000 

Is  to  difference  of  latitude         7.55      0.8779^ 
So  is  fecant  bearing  4.2,8       10.00132 

10.87937 
10.00000 


To  the  diftance  7.57  0.87927 

I  have  fet  down  the  operations  in  full,  for  finding  the 
bearings  and  diftances  of  the  two  firft  lines,  as  the  diffe 
rence  of  latitude  of  one,  and  the  departure  of  the  other, 
is  lefs  than  unity,  (fee  page  55)  and  made  that  fide  of  the 
fuppofed  triangle  radius,  which  is  more  than  unity ;  pro 
ceed  with  the  difference  of  latitude  and  departure  of  the 
other  lines,  as  before  direfted,  and  the  feveral  bearings 
and  diftances  will  be  found,  as  in  the  preceding  traverfe 
table.  Thefe  operations  will  be  profitable  for  the  learner 
to  work  in  full. 

The  foregoing  is  the  beft  method  of  finding  the  area  of 
a  piece  of  land  taken  by  interfe&ions  ;  but  for  the  fake  of 
fome  variety,  enlarging  the  ideas,  and  ripening  the  iudg- 
ment  of  the  learner,  I  ftiall  find  the  area  of  the  preceding 
by  Problem  10,  page  108,  and  firft  find  the  area  of  the- 
triangles  formed  from  the  point  I,  to  thefe  corners  of  the 
field  which  include  no  part  of  the  Map ;  and  then  to  thofe 
including  the  Map,  and  the  fum  of  the  outward  triangles 
taken  from  that  of  the  inward,  will  leave  the  double  area 
of  the  Map. 


OF     INTERSECTIONS. 

To  find  the  area  of  IAGI. 


197 


As  radius 
Is  to  IA  7 
IGJ 
So  is  fine  [  I 

90° 

29-47 
18.27 
31.30 

IO.OOOOO 

1.46938 

1.26174 
9.71809 

12.44921 

IO.OOOOO 

To  double  area 

281.33 

2.44921 

To  find  the  area  of  IGFI. 


As  radius 
Is  to  IG  1 

IF} 

So  is  fine  [  I 

9° 
18.27 
13.66 
13.30 

IO.OOOOO 

1.26174 

1.13545 
9.36818 

*  1.76537 

To  double  aiea 

58.26 

10.00000 

i.76537 

To  find  the  area  of  IFEI. 


As  radius 
Is  to  IF  I 

IE) 

So  is  fine  [  I 

9° 
13.66 

22.23 
24. 

IO.OOOOO 

1.13545 

1.34694 
9.60931 

12.09170 

10.00000 

To  double  area 


2.09170 


198        OF    INTERSECTIONS. 
To  find  the  area  of  IABI. 


As  radius 
Is  to  IA  1 
IBJ 

So  is  fine  [  I 


To  double  area 


90. 
^9-47 
35-43 


IO.OOOOO 

1.46938 

1-54937 

9.37600 

12.39475 

IO.OOOOO 

2.39475 


To  find  the  area  of  IBCL 


As  radius 
Is  to  IB  7 
1C  } 

So  is  fine  [  I 

9° 

35-43 
29-83 
9-'5 

IO.OOOOO 

!-54937 
1.47465 
9.20613 

12.23015 

IO.OOOOO 

To  double  area 


169.9 


2-23015 


To  find  the  area  of  ICDI. 


As  radius 
Is  to  1C  1 
IDJ" 

So  is  fine  ^ 


To  double  area 


90 

29.83 

30-75 
19.30 


306,* 


ro.ooooo 
1.4,7465 
1.48784 

9-52350 
12.48599 

IO.OOOOO 

2.48599 


OF    INTERSECTIONS. 

To  find  the  area  of  IDEL 


199 


As  radius 
Is  to  ID 


So  is  fine  [  I 


To  double  area 


90 

3°-75 

26.30 


3°5 


IO.OOOOO 

1.48784 
1.34694 
9-64953 

12.48431 

IO.OOOOO 

2.4843  * 


IAGI 
IGFI 
IFEI 

IAGFEI 


Double  Area. 

281.331 
58.26  V  Add 

133.51.) 
463.10 


IABI 
IBCI 
ICDI 
IDEI 


Double  Area, 

248.17" 
169-90 
306.20 

305.00. 

1029.27 


From  IABCDEI 
Take  IAGFEI 
Leaves  ABCDEFGA 


Area  a8  A.  iR.  9.36?. 


Double  Area. 
1029.27 
463.10 

1)566^7 
A.  28,3065 


P.    9,3600 


2oo          OF      ATTRACTION. 

The  fmall  difference  between  this  method,  and  the  for- 
V2ner,  is  owing  to  fome  lofles  fuftairied  in  not  finding  the 
€xa&  number  anfweringtoa  logarithm,  and  to  the  advan 
tage  of  two  decimal  figures  in  the  difference  of  latitude 
and  departure,  in  working  the  traverfe  table ;  therefore 
the  firft  method  is  preferable. 


OF    ATTRACTION. 

IT  fomedmes  happens,  that  the  needle  is  attracted  out 
of  its  cuftomary  poiition,  by  an  unknown  caufe  ;  but 
moft  probably  owing  to  fome  matter  near  the  furface  of  the 
eauh :  as  it  is  frequently  observable  where  there  is  the  ap- 
peafance  of  iron-ftone;  and  this  attraction  will  frequently 
vary  in  quantity,  and  in  denomination,  at  every  ftation. 
Therefore,  to  take  the  bearings  truly,  where  the  needle 
is  attracted,  ob&rve  the  following  clire&ions  ;  as  for  ex 
ample. 

Suppofe  a  field,  bounded  as  by  the  Map  in  the  following 
page,  to  be  fo  fituated ;  a  true  furvey  of  which  is  required. 


AVe.  Particular  care  muft  be  taken  to  count  the  degrees  at  eve 
ry  ftation  from  the  fame  end  of  the  needlet ;  as  in  this  exam 
ple,  I  count  from  the  north  end. 


OF     ATTRACTION; 


* 


.  The  dotted  lines  reprefent  the  Magnetic  points. 

Seek  a  place  where  two  ftations  can  be  taken,  without; 
attra&ion ;  this  may  be  tried  and  proved  by  back-fights, 
and  the  nearer  to  one  corner  of  the  field  the  better,  whe 
ther  within  or  without  the  inclofure,  as  for  inftance  ;  fup- 
ptfe  I  fetmy  inflrument  at  G,  and  take  the  bearing  to  H?* 

D  d 


OF     ATTRACTION; 

and  then  by  aback-light  frcmH  to  G,  the -bearing  is  the 
fame ;  therefore  no  attra&ion  at  either  of  thcfe  Rations. 
Then  from  H,  I  take  the  bearing  to  A,  one  corner  of  the 
field,  and  it  is  N  25°  W;  then,  by  aback-light,  H  bears 
from  A,  S  23°  ^E  ;  therefore  at  A,  the  north  point  of 
the  needle  is  attra&ed  a -J  degrees  wefterly^  then  turning 
the  lights  to  B,  it  bears  N  40°  \  W:  to  this,  add  the 
-atta&ion  2  \  degrees,  and  it  gives  the  true  bearing  N  43° 
W ;  diftance  meafured  is  7  chains,  2,0  links.  Then,  by  a 
back-light,  A  bears  from  B,  S  46°  E ;  therefore  the  north 
point  is  attra&ed  3  degrees  eafterly  at  this  place ;  then 
turning  the  lights  to  C,  and  it  bears  N  45°  \  E;  and  aba 
ting  three  degrees,  the  attra&ion,  it  leaves  the  true  bear 
ing  N  42°  JE,  7  chains,  28 links;  then,  by  aback-light, 
B  bears  from  C,  S  40°  W :  hence  at  this  ftation,  the 
north  point  is  attracted  2  \  degrees  wefterly  ;  then  turn 
ing  the  fights  to  D,  it  bears  N.  a  J  E.  and  the  atta&ion 
being  abated,  makes  it  a  due  north  courfe,  4  chains,  10 
links  ;  then,  by  a  back-fight,  C  bears  from  D,  S.  4°  W. 
Hence  the  north  point  here  is  attracted  4  degrees  weftely  5 
then  turning  the  fights  to  E,  it  bears  S.  57°  \  E.  from 
which  take  the  attraction,  and  it  leaves  the  true  bearing, 
S.  53°^,  E.  10  chains,  .75  links;  then,  by  a  back-fight, 
D  bears  from  E,  N.  50  W.  therefore,  here  the  north 
point  is  attracted  3  j  degrees  eafterly  ;  then,  turning  the 
fights  to  F,  it  bear,  S.  18  E.  to  this  add  the  attra&ion 
3  I  degrees,  and  it  gives  the  true  bearing,  S.  31°  *,  E. 
8  chains,  97  links  ;  then,  by  a  back-fight,  E  bears  from 
F,  N.  19°,  £  W,  hence  the  north  point  here  is  attra&- 
ed  two  degrees  wefterly  j  then,  turning  the  fights  to  A, 


OF      ATTRACTION.  -03 

the  place  of  beginning,  it  bears,  N.  89  W.  From  this, 
take  the  attraction,  and  it  leaves  the  courfe  to  be  due  weft, 
ii  chains,  93  links. 

Hence,  the  true  field  notes  are, 

Ch. 

AB  N.  43°    W.  7.20 

EC  N.   42  i  E.  7.28 

CD  North.        4.10 

DE  S.  53  |  £.  10.75 

EF  S.  21  £    E.   8.97 

FA  Weft.         11.93 

Area  13 A.  3R.  34?.+ 

Gare  muft  be  t alien  to  have  things  in  good  order ;  the 
needle  muft  traverfe  well,  theinftrument  fet  level,  a fmaU 
ftraight  rod  to  take  the  fights  to,  and  that  fet  perpendicu 
lar,  otherwife  inaccuracies  will  arife. 

The  attra&ion,  when  wefterly,  and  the  next  ftation  is  to 
the  weftward  of  the  meridian,  then  the  attraction  muft  be 
added  to  the  bearing  given  by  the  needle,  for  the  true 
bearing ;  but  if  the  next  ftation  be  eaftward  of  the  meri 
dian,  then  the  attra&ion  muft  be  taken  from  the  bearing 
given  by  the  needle  for  the  true  bearing :  fo,  when  the 
attra£lion  is  eafterly,  and  the  fucceeding  ftation  eaftward 
of  the  meridian,  then  the  attraction  muft  be  added  to  the 
bearing  given  by  the  needle  for  the  true  bearing;  but  if  the 
ftation  be  weft  of  the  meridian,  then  the  attraction 


-04  OF    ATTRACT  ION. 

mud  be  taken  from  the  bearing  given  by  the  needle  for  the 
true  bearing  between  the  prefent  arid  next  flations. 

Thefe  obfervations  being  ftri&Iy  attended  to,  the  bear 
ings  of  a  field  may  be  truly  taken,  where  the  needle  is  at- 
trafted  ;  although  the  ftatipn,  as  at  H,  be  fo  remote  from 
the  land  to  be  furveyed,  as  to  require  feveral  flations  and 
eourfes  to  arrive  at  one  corner-of  the  field*  -  > 


VARIATION. 

It  is  well  known,  that  there  is  a  Variation  in  the  Neev 
die,  from  pointing  due  North  and  South ;  and  this  variacL 
on  is  continually  progreflive.  Hence  it  is,  that  the  bear- 
ings  of  lines,  taken  fome  years  ago,  and  the  prefent  time, 
do  not  agree  ;  therefore,  to  find  the  difference  between 
them,  or' the  true  bearing,  at  the  prefent  time, 

Run  the  line  according  to  the  given  bearing,  and  ob- 
ierve  the  nearefl  dillance  between  the  line  fo  run,  and  the 
corner.  Then  

As  the  length  of  the  whole  line, 

Is  to  57.3  degrees  ; 

So  is  the  faid  diftance, 

To  the  difference  of  variation  required. 

£  X  A  M  P  L  E, 


OF     ATTRACTION.  205 

EXAMPLE. 

Suppofe  a  line,  fome  years  ago,  bore  N.  45°  E.  di- 
ilance  20  chains  ;  and  in  running  this  line,  by  the  given 
bearing,  the  corner  is  found  2,0  links  to  the  left  hand. 

Required  the  bearing  at  the  prefent  time, 

Ag   f  Ch.       Deg.     Links.      Q     , 

J_  2,0  .  .  57.3.  :  :  2,0  .  .  o  34  to  be  abated* 

Hence  the  bearing  is  N.  44°  16 '  E. 

This  rule  is  fufficiently  exa&  in  common  pra&ice,  where 
the  bearing  and  meafure  were  both  true  ;  but  in  fome  old 
furveys,  there  are  great  inaccuracies :  Therefore,  the 
beft  way  is,  after  running  on  the  given  bearing  a  conveni- 
nient  diftance,  to  take  the  bearing  and  diftance  to  the  fuc- 
ceding  corner.  Then  find  the  bearing  and  diftance  be 
tween  the  corners,  as  taught  in  Diviiion  of  Land,  and  in 
Jnteri'e6lions9 


T  o 


T    O 

Survey  with  the  Chain  only. 


f  A  F  I  E  L  D  fo  fituated,  that  all  the  angles  can  be 
jfjL  feen  at  one  view,  may  be  accurately  meafured  by 
the  Chain  only.  As  for  inftance,  fuppofe  a  field,  or  piece 
of  land,  bounded  as  in  the  following  figure! Then, 

Meafure  from  B  to  G,  6  chains,  arid  perpendicular 
thereto  meafure  a  A  2  chains,  20  links,  and  perpendi 
cular  to  BG,  meafure  c  C  2  chains,  27  links,  and  Be  i 
chain,  14 links;  thenCE  4  chains,  21  iinks,  and  perpen 
dicular  thereto  dD,  3  chains,  19  links.  Again;  perpen 
dicular  to  BG,  meafure  hE  4  chainsf  90  links,  and  perpen 
dicular  thereto  gF,  89  links,  and  hG  I  chain,  53  links  ; 
then,  confequently,  h  c  will  be  3  chains,  33  links'  j  hg  be 
ing  rneafured,  will  be  3  chains,  2,0  links,  leaving  gF  i 
chain,  70  links.  And  as  each  line  is  meafured,  draw  it 
on  paper  with  a  pencil,  and  the  feveral  angles  by  the  eye, 
marking  each  line  with  its  own  diftance.  This  rough 
draught  will  greatly  aflift  the  memory  in  calculating. 

By  the  preceding  Problems,  the  area  of  the  feveral 
triangles,  &c.  will  be  found  to  be—-  - 


TO  SURVEY  WITH  THE  CHAIN. 


Sqr.  Ch. 

ABGA  6.6000 
BCcB 
CDEG 
EFgE 

FGhgF  3.87 zo  |B    pmb>        a^e  I07 

CEhcG  11.938053    ' 


3.117540  =  3 A.  oR.  I-3.3P.  4 


E  c 


fO  SURVEY  WITH  THE  CHAIN. 


By  meafuring  Ba,  and  Cd,  with  thofe  already  made,  a 
true  Map  of  the  field  may  be  conftnl&ed.  For  BG,  being 
laid  down  from  a  fcale  of  equal  parts,  and  a  A,  from  the 
fame  fcale,  it's  proper  diftance  from  B,  will  determine  the 
point  A,  and  the  perpendicular  cC,  will  fix  the  point  C  ; 
then  with  cE  in  the  compares,  and  one  foet  in  C,  de- 
fcribe  an  arch,  as  at  E  j  and  with  hE  in  the  corapaffes, 
and  one  foot  in  h,  interfe&  the  arqh  at  E,  which  fixes  the 
point  E,  and  the  perpendicular  dD,  it's  proper  diftance 
from  C,  determines  the  point  D  ;  then  from,  g  lay  off  the 
perpendicular  gF,  and  draw  the  lines  AB,  BC,  CD,  &c. 
and  a  Map  of  the  Field  is  completed. 

Admit  a  ijeld  bounded,  as  in  the  following  figure  ;  the 
dimenfions  of  which  are,  AB  27  chains,  35  links  ;  BC 
22  chains,  2,0  links;  CD  29  chains,  25  links;  DE  23 
chains,  70  links;  and£A3i  chains,  15  links:  The  dia 
gonal  BE  38  chains,  and  EC  40  chains,  10  links  ;  and 
from  this  meafure  it  is  required  to  make  the  Map,  and 
jfi  nd  the  area  thereof. 

To    MAKE    TH  E    M  A  P. 

Draw  AB  h's  proper  length  ;  then,  with  the  diagonal 
BE  in  the  cempafTes,  and  one  foot  in  the  point  B,  defcribe 
an  arch  at  E  ^  then  take  AE  in  the  compafles,  and  with 
one  foot  in  A,  crofs  the  former  areh,  and  the  place  of  in- 
terfe&ion  fixes  the  point  E.  Again  ;  take  EC,  and  with 
one  foot  in  E,  make  an  arch  at  C;  then,  with  BC,  and 
one  foot  in  B,  interfect  the  arch  at  C,  which  fixes  that  point. 
Again  ;  with  CD  in  the  compailes,  and  one  foot  in  C,  make 


TO.  SURVEY  WITH  THE  CHAIN. 


an  arch  at  D  ;  then,  with  DE,  and  one  foot  in  E,  inter* 
fed  the  arch  at  D,  for  the  point  D.  Laftly  ;  draw  lines 
from  point  feo  point,  and  the  Map  is  made.  Draw  the  di- 
gonals,  and  the  Map  is  divided  into  three  oblique  angled 
triangles.  Then  divide  each  of  thefe  into  two*  right  an 
gled  triangles,  by  Cafe  6,  Oblique  Angled  Trigonometry 
thus  -  - 


As  the  fum  of  B  a,  and  a  E  38 
Is  to  the  diff.  of  AB  and  AE  3,8 
So  is  their  fum  58.5  1.767*6 


3.34694 
*-57978 

* 


To  the  diff..  of  B  a,  and  a  E     5.85      0.76716 


From  half  the  fum  of    B  a,  and  a  E.         ig 
Take  half  their  cuff.  f^ 

Remains  the  leaft  bafe  B  a  16.08 


(See  the 


s.  33        TO  SURVEY  WITH  THE  CHAIN. 
D 


Then  AB  27.35  X  37.35=  748.0325,  and 
Ba  16.08  x  16.08  =  258.5664. 

From  the  fquare  of  AB,  take  the  fquare  of  B  a,  leaves 
489.4561,  the  fquare  of  Aa:  the  fquare  root  of  which, 
is  22  chains,  12  links  =  Aa.  Thus  proceed  with  the 
others,  and  they  will  be  found  as  in  the  figure. 

Sqr.  Ch. 

Area  of  ABEA,  is     420.28  byProb.  6,  page  104. 
BCDEB,  is  756.687  by  Prob.  8,  page  io6. 


1  17.6967  s 


.  2R.  31.473?* 


F.I   N    I 


TABLES 


o  r 


DIFFERENCE 


O   F 


LATITUDE  AND  DEPARTURE;: 


CONSTRUCTED 

TO  EVERY  QUARTER  OF  A  DEG&EE 
OF  THE  QUADRANT, 

AND  CONTINUED  FROM  ONE,  TO  THE 

DISTANCE  OF  ONE  HUNDRED 

MILES  OR  CHAINS. 


WILMINGTON: 
BY  BONSAL  AND  NILES,  FOR  ZACHARUH  JES»» 


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s  9 

TRAVERSE  TABLE- 


35 

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61 

60,96 

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62 

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64 
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63,962,23 
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3,66 

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84 

85 

84,95 

2,97 

84,93 

3,34 

84,92 

84,90 

4,08 

85 

86 

85?95 

3,00 

85,93 

3,38 

85,92 

3>75 

85,90 

4,13 

86 

87 

86,95 

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3,42 

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3,79 

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4,17 

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3,07 

87,93 

3,45 

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3,84 

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3,28 

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96,894,65 

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3,46 

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97,894.70 
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98 
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90.92 
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Lat 

OQv9i 

4,36 
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99,884,80 
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35     £ 

ss 

88  Deg. 

875-  Deg. 

87^  Deg. 

87!  Deg. 

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T  R  A  V  E  R  S  E     T  A  B  L  L. 


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5  t 

T  R 


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T  R  A  V  E  R  S  E    T.  A  B  L  E. 


n  c 


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23 

24 

25 
26 
27 
28 
29 

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3i 

32 
33 
34 

3.5 
36 
37 
38 

30 
40 

42 

43 
44 
45 
46 
47 
48 

49 


Deg. 

Den 


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0,14 

0,21 


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9,9? 


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4,96 
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16.96 


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21,95 


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5,9 
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36,89  ,9°  I  36  87 
37,882,98  37,87 


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47,843  971 
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TRAVERSE    T  A 


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64,82 

4,82 

64,8 

5,10 

64.78 

5,38 

65 

66 

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4,89 

65,80 

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66 

67 

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4,67 

66,82 

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68 

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68 

69 

68,83 

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5,34 

71,78 

0,67 

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72 

73 

72,82 

5,  '-'9 

72,80 

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72,77 

5,73 

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6,04 

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73,82 

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73,8c 

5,48 

73,77 

73-75 

74 

75 

74,82 

5,23 

74,79 

5,56 

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5-88 

74,74 

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75 

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75,81 

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75,79 

3,63 

75,77 

5,96 

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6,29 

76 

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76,81 

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80,80 

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80.72 

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82 

81.80 

81,75* 

6,08 

81,75 

6,43 

81,72 

6,79 

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82.90 

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6,87 

83 

84 

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84,79 

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85,7;: 

5.75 

85,70 

7.12 

86 

87 

8^79 

6,07 

86/7? 

6.4.5 

86,73 

6,83 

86,70 

7,20 

87 

88 

Ig7* 

6,17 

87.76 

6,52 

^7,73 

6,90 

8^,7 

7:29 

88 

89 

6,21 

88^76 

6,60 

88,73 

6,93 

88,70 

7,37 

89 

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89^.78 

6.9-8 

80  7,5 

6.6- 

89  .  7  2(7.  f  6 

89,60 

7,45 

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90,78 

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90,75 

6,74 

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7,14 

90,60 

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91 

92 

9t,78|6,42 

9',75 

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91,79 

7,22 

91,68 

7,6'.: 

92 

93 

92,776,49 

92,74 

6,39 

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93 

94 

93,776,56 

93,74)6,97 

93  7  ^ 

7,38 

93,68 

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1    9-5 

94,  76.63 

94'74!7>°4 

94,71 

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95-74 

7,11 

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96 

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96,766,77 

96,73 

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96,70 

7,61 

96,67 

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97,766,84 

97,73 

7^2(> 

67,7< 

7,69 

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8,12 

98 

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98,766,9* 

98,73 

7^34 

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7-77 

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09,69 
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12  5 

5   Deg.    ||    si    De*.i|    5-|  D,*. 

5  1    De£' 

C  JT 

?  ^ 

t^. 

Den!)  Lai. 

Dep  ||  i  at. 

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4,89 

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51 

52 

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4-53 

4-76 

5»»  76 

4,98 

51,7 

5,21 

52 

53 

52,8 

4,62 

52»7* 

4,85 

52,76 

5,°8 

5^,7 

5,3! 

53 

54 

53.79 

4,7' 

53,77 

4'94 

53,75 

5»i8 

53,7 

5»4i 

54 

55 

.54^79 

4,79 

54,77 

5.°  3 

54,75 

5,27 

54,7 

5-5' 

55 

56 

55,79 

4,88 

55.77 

55»74 

5,3^7 

55,7 

5,6i 

56 

57 

56.78 

497 

5.22 

56,74 

5,46 

56.7 

5.71 

57 

58 

57,78 

57.  7t 

57.7; 

5-56 

57,7 

5,8i 

58 

59 

58,7^ 

5,14 

58,75 

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58,73 

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5,91 

59 

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59-75 

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6,01 

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61 

60,77 

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60,74 

60,72 

j,8_5 

60,65 

6,11 

61 

62 

61,76 

5,40 

6i.74 

5,67 

6,,7 

5,94 

61,60 

6,91 

62 

63 

62,76 

5»49 

62.7. 

5^76 

62,71 

6,04 

62,68 

6.31 

63 

64 

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5,58 

63,7J 

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63,68 

6,41 

64 

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64'75 

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64.73 

5'95 

64,70 

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6,51 

65 

66 

5,75 

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6,04 

65.70 

65,67 

6,61 

66 

67 

66^75 

5  84 

66,72 

6,13 

66,69 

6,42 

66,66 

6,71 

67 

68 

67,74 

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67,71 

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6,8  1 

68 

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68,74 

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68,71 

6,31 

68,68 

6,61 

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69 

70 

69,73 

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6,41 

60.68 

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70 

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6,19 

70,70 

6,5> 

70,67 

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70.6^ 

7.11 

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72 

71,73 

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72 

73 

72,72 

6,36 

72,69 

6.68 

72,66 

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72,6; 

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73,72 

6,45 

73,69 

6,77 

73,66 

7,09 

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74 

75 

74,71 

6,54 

74,  6Q 

6,86 

74,65 

7,19 

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75 

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6,62 

75,68 

6,95 

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7,28 

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7^61 

76 

77 

76,71 

6,71 

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7,05 

76,65 

7,38 

76,61 

7,7l 

77 

78 

77-7° 

6,80 

77,64 

7,48 

77.61 

7,8i 

78 

79 

78,70 

6,89 

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78,64 

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78,6c 

7.91 

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70,66 

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81 

80,69 

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82 

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81,59 

8,22    82 

83 

82,68 

7,23 

82,65 

7-59 

82,62 

7,96 

82,51 

8,32  83 

84 

83,68 

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83,65 

7,69 

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86 

85,67 

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85,64 

7,87 

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3,24 

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87 

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97,63 

8,54  i  97,50 

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98,62 

8,63     98,59 

3.06     98,54 

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£C!&K5;====«5=^^                                                                   3? 

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TRAVERSE    TABLE. 


16 
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18 
19 

20 
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22 

23 
24 

25 

26 
27 

29 

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32 
33 
34 
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41 
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8 
9 

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12 

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17 
18 

20 
21 
22 

23 
04 

26 

27 
28 
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32 
33 
34 
35 
36 
37 
38 
39 
4.0 

42 
43 
44 
45 
46 

47 
48 

49 


R*aa^ 


TRAVERSE    TABLE, 


*5 


^6 

6    De£. 

6i  He*. 

6|-  Bes. 

6^  Deg. 

|.c 

^  F 

Lat.  )lJtp. 

Lit.  jD-u. 

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51 

50.72    5:33 

50,7° 

5,55 

50,67 

5,77 

50,65 

5,99 

53 

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51,72 

5,44 

51,69 

5,66 

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5,89 

5  ',64 

6,1, 

52 

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52,71 

5-54 

52,68 

5,77 

52,66 

6,00 

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6,23 

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53.7°|  5,64 

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5,88 

53,65 

6,11 

53,63 

6,35 

54 

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54.67 

5,99 

54,65 

6.23 

54,62 

6,46 

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55^9   5  85 

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6,10 

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6,34 

6.58 

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56,61;    5.96 

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58,65 

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58,62 

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60,67'    6.38 

6,564 

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6,91 

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62 

63 

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62,65 

6.59 

61,63 

62,63 

6,75 
6,86 

61,60    7,02 
62,60    7,13 

61,;  7 
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62 
63 

64 

63,65 

6,69 

63,6* 

6,97 

63,59 

7,25 

63.56 

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64 

65 

64,64 

6,79 

64,61 

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64:58 

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64-55 

7,64 

6  5 

66 

65,64 

6,9° 

65,61 

7,19 

65-58 

7,47 

65,54 

7,76 

66 

67 

06,63 

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66,60 

66.  57 

7,58 

66,^4 

7,88 

67 

68 

67,63 

7,1  1 

67,60 

7,4° 

67^6 

67,53 

7,99 

68 

69 

68,62 

7,21 

68,59 

68,56 

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68,52 

69 

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69,58 

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69,51 

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71 

70.61 

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70.5. 

8,35 

71 

72 

71.61 

7,53 

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7,84 

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8,15 

71,5° 

8-;  4  6 

72 

73 

72,60 

7,63 

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7,95 

8,26 

72,49 

8,58 

73 

74 

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73,56 

8,06 

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8,0? 

76,54 

8.38 

76,51 

8,72 

76,47 

9,°5 

77 

78 

77,57 

8,15 

77,54 

8,49 

77,5° 

8,83 

77,  46 

78 

79 

78,57 

8,26 

78,53 

8,60 

78,49 

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78,45 

9,29 

79 

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8.36 

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9,64 

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82,55 

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82,47 

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82,42 

9,76 

83  i 

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83,54 

8,78 

83,50 

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9,51 

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84 

85 

84,53 

8,88 

84,50 

9-25 

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9,62 

84,41 

9,99 

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9,36 

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86,52 

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86,48)  9,47 

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86,40 

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87,48 

9,58 

87,43 

9,96 

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TRAVERSE    TABLE. 


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£"g 

7  J 
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2,15 

16.  8<- 

2,22 

16.84 

2,29 

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17,86 

2,19 

17,86 

2,27 

17,85 

2,35 

17^84 

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2,48 

18,83 

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20,84 

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2,83 

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21,8, 

2,68 

21,82 

0,78 

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21,  80 

2.97 

22 

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2.80 

22.  8e 

1,90 

22,8, 

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22.79 

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23 

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2,92 

23,81 

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23-75' 

3,13 

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24.8 

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24.80 

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24.79 

5,26 

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25.81 

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25,79 

3,28 

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3,39 

25,76 

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26,8 

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26,78 

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26,77 

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27.78 

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27,76 

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28,77 

3,66 

28,75 

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3,70 

29.74 

3  .92 

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31 

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31.76 

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4,18 

3  1,71 

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32 

33 
3-1 

52,75 

33  5  /.? 

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32-7-1 
33»73 

i;29 

32,72 
33-71 

4>44 

32  7c 
33,69 

4«4.5 
4-58 

33 
34 

4.27 

34,  72 

4»42 

34,7< 

4,57 

34,68 

4,72 

06 

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1:39 

35*7  l 

4,54 

35,69 

4,7° 

35,67 

4,85 

36 

07 

36,?72 

36,7 

4,67 

36,68 

4,83 

4-99 

37 

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37,7-. 

[•63 

37,7'. 

4,80 

37-67 

4,96 

37^5 

5,17 

38 

38,71 

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38,69 

4,92 

38,67 

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38,64 

5,26 

39 

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39-7C 

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5.°5 

39-66 

C,22 

39?  63 

5?  39 

4' 
42 

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40.67 
41,66 

5-17 

4°,  65 
41,64 

5,35 
5,48 

41,62 

5-^6 

41 

42 

rr 

43 

^2,68 

3,24 

42,66 

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5,6i 

42i61 

5  8t 

43 

44 

43/^7 

5,36 

43,  65 

3,5.5 

43,62 

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43,6o 

5-93 

44 

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44567 
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5,61 

44.64 
45563 

5,1? 

44,62 

6,00 

44,59 
45,5?' 

6,0  7 

),2O 

45 
46 

'    47 
48 

49 

46,65 
47j64 
48,63 

5,73 
5,2? 
5.97 

47,62 
48,61 

6,06 

6,18 

46,60 

47-59 
48,58 

9,13 
6,27 
6,40 

4^56 
48,55 

6,34 
6,47 

47 
48 
49 

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9.6-': 

6,09 

49,6 

6.31 

49*57 

6,53 

42,54 

6.74 

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82  f  i-e^. 

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83    D?.g.» 

82  1   Deg. 

82-1-   Peg- 

TRAVERSE    TAB  L'E, 


6,35 
88  7,34 
89,88,34 

22§2i3 

91  9°:32 

9291,31 
9392:3i 
9493,3° 
n  £  9  4- , 2  Q 

9695,^ 
9796,28 

9«97,^j 
53998,26; 
10099,25: 

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12.07 


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90,2714,48 

91.26^  i. 61 

92,26^  1,74 
93.2^!!  1.86 

95,23:12.12 

96,22)12.24 

97,22  :2, 37 

98,2i;ia,49 
99. S"  12,62 
DepJLat 


90.22  11,88 


91.21 


92,26 

9332- 


94,1912,40 


9.3,i8 
96,17 
97,16 

98,15 
99,14 
Dtp. 


12,01 


12,14 

12,27 


12.53 


12,79 

12,92 


82^  Deg. 


88,19   12,0'C 
89.18  lg.14 


91,16 


9J.M 

3.6,' i  i 
97»io 
98,10 
.03.09 


12-.41 

12.68 

18)81 

12,95 

13,08 


jo '49 

LjHf  • 


82!  Deg. 


T  R  AVERSE    T  A  B  L  E. 


IP 

8  Deg.    IJ 

m 

Lat. 

$£• 

D.ep 

=-••  -=«==s=- 

8^-  Deg. 
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if 

Lat.  J 

3ep  1 

Lat. 

D-p 

I 

0,99 

>§14 

0,99 

3,14 

0,99 

3,15 

0,99 

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1,98 

5.28 

1,98 

1,98 

3.30 

1,98 

3,30 

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2,97 
3,96 

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2,97 
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2,97 

3,95 

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4,95 

9,70 

4>95 

0.72 

4,95 

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3,84 

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5,9.- 

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6 

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6,93 

3,97 

6/93 

1,00 

6,92 

1,03 

6.9^ 

1,0.6 

7 

8 

7,92 

1,11 

7,92 

1,15 

7/91 

J    ;    1    8 

1,22 

8 

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8.91 

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8,91 

1,29 

8,9' 

1,33 

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9 

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J»$? 

1.39 

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T..52 

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10,89 

1.53 

10,89 

1,58 

io.88 

1,63 

ii>,8? 

1,67 

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12 

11,88 

1,67 

11,88 

1,72 

1.77 

11.86 

1,8S 

12 

13 

12,87 

1,  8l 

12,87 

1,87 

i2!,86 

1,92 

12.85 

I.98 

13 

14 

13,86 

*,95 

13,86 

2,01 

13,85 

2,07 

13-84 

2,13 

H 

15 

14,851 

2,04 

14,85 

2  J  1  5 

14,84 

2,22 

i  ^}8c 

2,28 

15 

16 

15,84 

",23 

15.84 

2.30 

15,82 

15,81 

2.43 

16 

17 

16,83 

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16,83 

2,44 

16,81 

2,5! 

16.80 

17 

18 

T  ^-      Q 

2,5i 

17,81 

2,58 

17,80 

2,66 

17,79 

2,74 

18 

19 

18,82 

2,64 

18,  8c 

2,81 

18,78 

2.89 

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20 

10,81 

2y7_8 

19,79 

2,87 

19,78 

2,96 

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3  o^ 

20 

2  1 

20,80 

2.92 

2o!78|3,oi 

20.77 

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20,76 

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21-79 

3,°6. 

21,77  3>*6 

21,76 

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21,74 

3.55 

22 

23 

22,78 

J..2C 

22,763,30 

3,4° 

22,73 

23 

23,77 

3-34 

23,75  3»44 

23'  74 

"«55 

23,72 

3^65 

24 

25 

24576 

3,48 

24,74'3-59 

3>7° 

24.71 

3,80 

25 

26 

25,75 

3,62 

25,733*73 

25.71 

3,84 

25,703,96 

26 

27 

26.74 

3,76 

26,7*3,87 

26.70 

26,69!4,u 

27 

28 

27.73 

3-9° 

27.714,02 

27.69 

4^4 

27,67 

4,26 

28 

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28^72 

4,04 

28,704,16 

28.68 

28,66 

4,41 

29 

30 

29.71 

M8 

4?3i 

59,69 
3o;68 

4.30 
4,45 

29.67 
30,66 

4^43 

29,65 
3°564 

4.56 

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3l 

3°,7° 

4,72 

32 

31,69 

4i45 

31  67 

4-<9 

3^65 

4-7S 

31,63 

4-87 

3« 

33 

32.63 

32,66 

4>74 

32,64 

4-88 

32,62 

5»02 

33 

34 

33,67 

4^73 

33,65 

4,88 

33,60 

5,»7 

34 

35 

34;66 

34.64 

5>02 

34.61' 

5,17 

34,59 

5832 

35 

36 

35.65 

5>ci 

35*6^ 

5,  17 

35,6^ 

5"32 

35>58 

5,48 

36 

37 

36,64 

5,15 

36,62 

5.31 

36,59 

5-47 

36.57 

5-63 

37 

38 

37,63 

0,29 

37,61 

5,45 

5,62 

37-56 

5,78 

38 

39 

38,62 

5-43 

38,60 

38,57 

5,76 

38-55 

5,93 

39 

40 

39.61 

•>»«37 

39,55 

M.4 

39,56 

5,91 

31,53 

6,  8 

41 

40.60 

r7>7l 

40,58 

5,88 

40,55 

6.06 

4°i52 

6,24 

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42 

$'!,£« 

5,85 

4i  57 

6,03 

6,21 

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6,39 

42 

43 

42,58 

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42,56 

6,17 

42^5<- 

6,36 

42,50 

6,54 

43 

44 

43,5' 

^.12 

43.54 

6,31 

6.50 

43  49 

6.69 

44 

45 

44-56 

6^26 

44,5£ 

6,46 

44,51 

6,65 

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45 

46 

45:55 

6,40 

45,52 

6,60 

45,45 

6,80 

4^,467.0' 

46 

47 

46,54 

6,54 

46.51 

6,74 

46.48 

6  95 

46.457,15 

47 

48 

47,53 

6,68 

47.50 

6,8§ 

47,47 

75°9 

47.44  tw 

48 

49 

5,82 

48}49 

7,°3 

48,46 

48,43  7,45 

49 

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49»5! 

6  96 

7.17 

49.45 

7^39 

49,42  7.6 

JjO 

Dtp 

LIT.  ||  Dep. 

i^a,. 

Uc-p. 

Lat. 

Drp/Lat 

«  i 

u§ 

SaDeg.    |J8iJ    Deg 

8  1  i  Deg. 

SiABeg. 

S'c 

TRAVERSE    TABLE. 


V.VJ.B* 

3Sj 

8  Deg. 

81    Deg. 

8i  Dejj. 

*&l 

£ 

Lat. 

Dep. 

LaTT 

Dep. 

LM. 

Dep. 

Lat. 

Dep. 

p=  c 

5» 

-0,50 

7,ro 

5°»47 

7.32 

50.44 

7»54 

50,41 

7,76 

5i 

52 

5  '.49 

7,24 

51*46 

7,46' 

51,43 

7,69 

5*>39 

7,9J 

52 

53 

7,38 

52,45 

7>6i 

52,42 

7,63 

52,38 

8,06 

53 

54 

53>47 

7,5* 

53:44 

7,75 

53,41 

7,98 

53,37 

8,21 

54 

55 

54»46 

7365 

54,43 

7,89 

54,40 

8.13 

54,36 

8,37 

55 

56 

5,46 

7.79 

55,42 

8,04 

55,38 

8,28 

55,oi> 

8,52 

56 

57 

6,45 

7,93 

56,41 

8.18 

5*6,37 

2.43 

36,18 

8,67 

57 

58 

7,44 

8,07 

57,4° 

8,32 

57,  36 

3,57 

57,  3i- 

8,82 

58 

59 

8,43 

8,21 

58,39 

8,47 

58,35 

8.72 

58^^' 

8,98 

59 

60 

9,42 

8,35 

59,38 

8.61 

8^87 

59;^^ 

61 

0,41 

8,49 

60,37 

8,7.5 

6  >,33 

9,U,2 

60,29 

9.28 

61 

62 

1,40 

8:63 

61,36 

8,90 

61,32 

61.28 

9)43 

62 

63 

2,39 

8.77 

62.35 

9,04 

62,31 

9,31 

62,27 

9.5S 

63 

64 

63.38 

8,91 

63^4 

9,18 

63.30 

9,46 

63,26 

9,74 

64 

65 

4.37 

9,05 

64,33 

9,33 

64,29 

9,6r 

64,24 

9389 

65 

66 

5,36 

9,19 

65,32 

9>47 

65,28 

9,76 

65,23 

10,04 

66 

67 

66,35 

9?32 

66,31 

9,61 

66,26 

9,9° 

66,22 

0,19 

67 

68 

7,34 

9.46 

67*30 

9*76 

67,25 

10,05 

67,21 

68 

69 

8,33 

9,60 

'68,29 

9.9° 

68,24 

68,20 

o'5o 

69 

70 

_2?32 

9,74 

69,28 

60.2,^ 

i   .35 

6_0j*9 

10,64 

TO 

71 

9,88 

70,27 

10,19 

70,22 

1  0,49 

70,17 

0.8 

72 

''3 

0,02 

71^5 

£0.33 

7I.2J 

JO,  64 

71,16 

io,95 

72 

73 

2,29 

0,1  6 

72,24 

10.47 

72,20 

10,79 

72,15 

11,10 

"3 

74 

.3,28 

o.3«> 

73  -»3 

10,62 

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11,26 

74 

75 

74,27 

0,44 

74,22 

0,76 

74,18 

n,<.9 

74,13 

11.41 

75 

76 

7.V26 

0,58 

10,91 

75,^7 

75,12 

11,56 

76 

77 

-6,25 

I  :,72 

76,20 

11,05 

76,15 

11.38 

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n,7i 

77 

78 

77  24 

10,86 

77.19 

11,19 

77,1^ 

11,53 

77«°c 

78 

79 

78,23 

io,99 

78,18 

'1-34 

78,13 

n.68 

78,08 

I«2,02 

79 

80 

79.22 

11,13 

Z2>17 

11.48 

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U,82 

79,07 

1^,17 

80 

81 

80,21 

11,^7 

8>,i6 

11,62 

8.1,1.1 

IX>97 

80,06 

12,32 

81 

82 

81,20 

11,41 

81,15 

u  77 

81,  i> 

U,I2 

8i,ot 

12,47 

82 

83 

82,19 

1  1,55 

82,14 

11,91 

82,rS 

12,27 

82,03 

I2S6. 

83 

84 

13,18 

11,69 

8  j  13 

12,05 

83,0^ 

83,02 

12,78 

84 

85 

84,17 

84,12 

12   20 

84,07 

12,56 

84.0 

12  9^ 

85 

86 

85,16 

11.97 

85,1 

12.34 

85,06 

12,71 

85,00 

13,08 

86 

87 

86,15 

12,11 

86,n 

12,48 

86,04 

12,86 

8599 

13,23 

87 

88 

87  14 

12,25 

87.09 

12,63 

87,0. 

r3»oi 

86,9b 

88 

89 

88,13 

12  39 

80,0* 

'2,77 

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1^,16 

87,9 

13,5^ 

89 

30 

89,12 

12,53 

89,07 

i  2,9  1 

§9_o 

13,3° 

88,9 

ig.6 

91 

90,11 

12.66 

90.0 

13,06  J90,o- 

!3;45 

89,9 

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9i 

92 

91,10 

12^80 

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13^20  I  90,90 

13.60 

9^,9 

I4;00 

92 

93 

92,09 

12,94 

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>3>34  3  9!;9 

13,75 

9^9 

r4'i5 

93 

94 

93i°9 

13,08 

93.°£ 

13.-49  |!  92,9 

13,89 

92,9 

14,  3c 

94 

95 

94,08 

13,22 

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13-63  !J93,9 

14,04 

93,8 

14,4^ 

95 

96 

95,07 

13.36 

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14,19 

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14.60 

96 

97 

96,06 

13,50 

96,00 

13,9*  I  9.5,9 

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97 

98 

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13,64 

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14.06  it  96,9 

14  49  II  56»8 

14,9 

98 

99 

98,04 

13,7$ 

97,98 

14*21  197  9 

14,63  ||  97.85 

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98,97 
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15,21 

lipo 

1  c*: 

,  gjl 

|Dep 

Lat. 

J.S 

82   Deg." 

8iJ   Deg.   11  8  1*  Deg.    ||    Sii'Deg.la 

^Q 

TRAVERSE    TABLE. 


Q  c 

Q  LV^M" 

9r    Deg. 

.  9i  ^g 

S  94  Beg. 

-*&ju 

D 

?     55 

Lat7~l>j7 

Lat^ 

Dep 

Lat.  jDe" 

tir; 

De 

p 

j 

v>,990,i6 

•  °.»9c 

0,990,  it 

o,9c 

0,1 

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2 

1.980,31 

1.97 

0,32 

1,97 

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1,97 

0,3 

2 

3 

2,960,47 

2,9L 

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2,96 

0.50 

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3-95 

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3»95 

0,66 

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0.6 

4 

5 

4,940,78 

4,03 

0,80 

4-93 

0,83 

4,93 

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5 

6 

5,92 

0.96 

5,92 

0,99 

5,9J 

1,0' 

6 

7 

6*9? 

1,10 

6,9' 

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6,90 

1,16 

6,9  c 

1,19 

7 

8 

7,9C 

1,25 

7,9.^ 

1,29 

7.89 

1,32 

7,88 

i,3. 

8 

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1,4.1 

8,88 

1.45 

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1,49 

8,87 

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10 

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1,61 

9.86 

1,6,5 

9,86 

1,6, 

10 

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10.86 

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1,82 

10.84 

1,86 

11 

12 

11,85 

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11,84 

i'93 

11,84 

1,98 

ii,8c 

12 

13 

12,  8^ 

2,03 

12,83 

2,09 

12,S-2 

2,'j, 

12,81 

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14 

13^85 

2,19 

13,82 

2,25 

13,8  ! 

2,31 

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"•3" 

14 

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14,8* 

2.35 

14,8 

2.41 

14,79 

2.48 

14,78 

2,54 

15 

16 

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2,<-Q 

15,79 

2,57 

15,78 

2,64 

15»77 

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16 

17 

167 

2,66 

16,78 

2,73 

2,8l 

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2,88 

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18 

1-7.7* 

2,82 

17.77 

2,89 

i17,  75 

2,97 

17,74 

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18 

19 

18,77 

2,97      i8,75 

3,<>5 

i8,74 

3,14 

3,22 

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20 

19,7/i 

3  1  1  3 

1  0,74 

3-21 

19,72 

3,30 

19,71 

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20 

21 

20,74 

3,29 

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3-38 

20,71 

3,4*7 

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2  1 

22 

21,  7. 

3,44 

21,71 

3-54 

21,70 

3,63 

21,68 

3'7c 

22 

23 

22,72 

'•  .60 

22.70 

3»'7° 

22,68 

3:  80 

22,67 

3>9° 

2  3 

23  7 

3',75 

23,69 

3,86 

23.6" 

3,06 

4,  of 

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26 

24,6f 

25,68 

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4,07 

24.67 
2j,66 

4,02 

4,18 

24.66 
25,6. 

4,  13 
4,29 

24,64 

4,40 

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26 

27 

26,67 

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26,65 

4,34 

26,63 

4,46 

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28 

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27,64 

4,  ro 

27,6? 

4^62 

27,60 

4^74 

28 

29 

28,6^ 

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28,62 

4,66 

28,60 

4,79 

28,58 

4,9i 

2  9 

32 

9.6? 

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£2,6.1 

4,82 

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59,5  7 

5,08 

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31 

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4.85 

30,60 

4,98 

30,57 

5,12 

30,55 

5^25 

31 

32 

5,01 

3^58 

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$1.56 

5,28 

3i»54 

32 

33 

2,59 

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32,55 

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32,52 

5,59 

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34 

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5,32 

33.  56 

5,47. 

33  53 

5>6i 

33,5  i 

5,76 

34 

35 

34,57 

5,48 

34,54 

5,03 

34,52 

7,78 

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5,93 

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35,56 

5,6-! 

3  5  >5  3 

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5»94 

35,48 

6,10 

36 

37 

$6,554 

5>79 

36,52 

5-95 

36j49 

6,11 

3<M7 

1,27 

37 

38 

5,94 

37.51 

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37.48 

6,27 

37,45 

6,44 

38 

39 

6,10 

3^,4C 

6,2.7 

38,47 

6,44 

38,44 

6,60 

39 

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32»5J 

6,26 

39.?  4  ^ 

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39S45 

6,60 

39,42 

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40,5" 

6.41 

40-47 

6.59 

4^,4-1 

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40.41 

6.94 

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41,48 

6,57 

4i,45 

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41,42 

5,92 

41,39 

7,11 

42 

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42,44 

5,9  1 

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7,28 

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43j46 

6,88 

43,43 

7,07 

43-4( 

7,26 

43,36 

7,45 

44 

45 

5.4,45 

7,04 

44.41 

7.23 

44,38 

7?43 

44,35 

7,62 

45 

46 

15,43 

7,20 

45:4 

7-39 

45,37 

7,53' 

45,34 

7,79 

46 

47 

16,42 

7,35 

46.39 

7-55 

46,36 

,/6 

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47 

48 

17,4i 

7,51 

47,38 

7,72 

47,34 

7  92 

47'S1 

3.  13 

48 

49 

48,410 

48.-  36 

7,88 

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48,29 

^3° 

49 

ii  .52. 

i,  s= 

19,3? 

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]a\ 

49,35 
Dep. 

VN4 
La.,  I 

49,32  8,25 
Dep.lLar. 

49,^8 

^47 

flp  rn 

8  1    J>g. 

80  5.  De<. 

boi    Deg. 

8oJ-  Deg. 

of 

T  R  A  V  E  R  S  E     TAB 


I  Peg. 
Lat.  jDep. 
50,26    8.64 


_  _  Lat,_ 
,20  fj  50,30 
36  -5i, 


65,14:10,6 
66,1310,77 


70,08 
71,06 

72505 

73-°4 
74,02 


71,95^30 
72,9311,50 

73,0212,70 
74,9012,87 
75,89  13.0 
76,87  13,21 


8402,97 
8583,9 


91,89,8 
92'9° 

9391 
9492,8 

9593* 
9694,8 

9795,8 
9896.7 
5997,7 


91, 6C 
92.64 
93^3 


s£S**< 


21 


TRAVERSE    TABLE. 


fcOfc 

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M,  •,  i  „  ,  ii._w>  «. 

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10  Deg. 

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2,95 

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10,83 

1,91 

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1,96 

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11,82 

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2,14 

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12.80 

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14,77 

2,60 

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16.74 

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18,71 

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18,70 

3,38 

18,68 

3,46 

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3,54 

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20 

19,7° 

3,47 

19,68 

3,56 

tq,67 

19.65 

3,73 

20 

21 

20,63 

3,65 

20,66 

3,74 

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20,63 

3,92 

21 

22 

21,67 

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21,65 

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21.6'*; 

4,01 

21,6l 

4.10 

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22,  6*, 

3,99 

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23,60 

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23,58 

4-48 

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4,34 

24,60 

4,45 

24,i8 

4,56 

24,56 

4,66 

25 

26 

25,6 

4,51 

4,63 

25,56 

4,74 

25,54 

4,85 

26 

27 

26,59 

4,69 

26,57 

4,80 

26,55 

4,92 

26,53 

5,04 

27 

28 

27,5' 

4,86 

27,55 

4,98 

5,10 

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i  27,51 

5,22 

28 

29 

28,5^ 

5,°4 

28,54 

5  5  1  6 

K&i 

5-28  j  28,49 

5,41 

29 

30 

29,54 

5«2I 

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5j3_4 

29,50 

5^7  I!  29,47 

5,60 

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3°»5. 

5,38 

5,59 

30,48 

5,6"5 

30,46 

5,72 

32 

31,5 

5,  56 

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5.  '69 

31,46 

5,83 

31*44 

5,97 

32 

33 

32,50 

5,73 

32,47 

5,87 

32,45 

6,01 

32.42 

6}i6 

33 

34 

33,4 

5,9° 

33,46 

6,05 

33,43 

6,20 

33,4C 

6,34 

34 

35 

34,4 

6,08 

34,44 

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34.41 

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34>39 

0,53 

35 

36 

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6,25 

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35,40 

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6:71 

36 

37 

36,44 

6,42 

36,4i 

6.58 

36,3? 

6,74 

36.35 

6,90 

37 

38 

37,4 

6,60 

37,39 

6,76 

37:  8  f 

6,92  j  37,33 

7-°9 

38 

39 

6,77 

38,38 

6,94 

38,35 

7,27 

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4° 

39-39 

6,QS 

39<3C 

7.12 

39,3^ 

7^29 

39J_ 

7,46 

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40,3s 

7,12 

40,35 

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40,31 

7,47 

40,28 

7,65 

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42 

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7,29 

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7,47 

41,30 

7,65 

41,26 

7,83 

42 

43 

42,3 

7,47 

42,31 

7,65 

42,28 

7,8.4 

42,25 

8,02 

43 

44 

43,3 

7,64 

43,3' 

7.23 

43,26 

8,02 

43,23 

8.21 

44 

45 

44,3 

7,81 

44,28 

8,01 

44,25 

8,20 

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8,39 

45 

46 

4dj3o|7,99 

45,27 

8,19 

45,23 

8,38 

45,!.  9 

8,58 

46 

47 

46,29 

8,16 

46,25 

8.36 

46.21 

46,18 

8,77 

47 

48 

47,27 

8,34 

47,23 

8,54 

47,20 

<^75 

47,16 

8,95 

48 

49 

48,26 

8,51 

48,22 

8.72 

48,18 

8,93 

48,14 

9,*4 

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$>  « 

49.248.68 
Dep.  Lat. 

49,208,90 
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49.16 
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La7. 

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80  Deg. 

79!-  D^g' 

79?    Deg. 

79i  i^g. 

aavj 

TRAVERS 


?.4  *       T  R  A  V  E  R  S  E     T  A  B  L  E. 


<s.     »  1C*- 

I}  C|  uDeg. 

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ii^r  Deg. 

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i,ar.   D  r 

Lai.  |Dep 

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Dep 

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Dep 

P 

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0,98 

2,19 

0,98 

3,20 

0.98 

0,20 

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0,20 

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1.96 

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3,39 

1,96 

3.40 

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3 

2,94 

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2,94 

3,59 

2,94 

3,60 

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3,76 

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3,98 

4.90 

1,00 

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6 

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1,20 

5,87 

1,22 

6 

7 

6,87 

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6,87 

1,37 

6,86 

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8 

7,85 

7,85 

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9 

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10,78 

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3,12 

15,68 

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15,66 

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16.69 

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3,59 

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18,62 

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20,61  4,01 

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31,33 

6,52 

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33 

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6.30 

32,37 

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32,3-1 

6,58 

32  31 

6,72 

33 

34 

33,38 

6,49 

33,35 

6,63 

33  32 

6,78 

33,29 

6,92 

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34,36 

34,33 

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34.30 

7-98 

34,27 

7,13 

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37 

35,34 
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6,87 

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37 

38 

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40,18 

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6,90 
17,11 
17-31 

17.72 
.'7.92 
,8.12 


•8,74 


19-35 


L-v 


.57 
5S 
59 

61 
62 

63 


66 

$7. 

68 

69 

7i 
72 
73 

74 

76 

77 
78 


8  i 

82 

83 
84 

;^6 
87 


S3 


26 


T  R  A  V  E  R  S  E     T  A  B  L  E. 


U      12  Deg.    j!  12!-  Deg. 

T  ->    i 

1  "     '3 

Deg. 

»•=£•-»  -^—  Jg^j 

«D^ 

a  g 

P  iLar.  |Dep.  1!  Lat.    D?p. 

La^.  !D?p. 

La:..    D'-p 

»  t?r 

i 

0,98!    0,21 

0,98,'    O,2l 

o,98j 

0,22 

0,98 

0,27. 

ir  ! 

2 

1,9^ 

0.42 

I»95j      °3-r2 

^95: 

0.43 

1,95 

°>44 

2i 

3 

2,93 

0,62 

2,93,  °v>4 

°,65 

2,93 

0,66 

3 

4 

3.91 

0,83 

3,9/j  °585 

3.91 

0,87 

3,90 

0,88 

4 

5 
6 

4,89 

5,8-7 

1,04 

4,89    1,06 
5,$6    1,27 

4,fe 

i  ,08 

4,88 

1^2 

i 

7 

6,85 

1,46 

6,84 

1,49 

M3 

1,52 

M'S 

1,54 

7 

8 

7,83    1,66 

7,82    1,70 

7,81! 

1.73 

7,8o 

1,77 

8 

9 

8,  So    1,87 

8,80    1,91 

8,79; 

1.95 

8,78 

1,90 

9 

10 

9,?8    2.08 

9,77^15 

.0.76; 

2.16 

9,75 

2,21 

10 

II 

10,76    2,29 

10,75!  2.33 

i°,74. 

"2f>S'8 

~~^7J 

1  1 

12 

12,74    2.49 

11,73    ",5,1 

11,  721 

a>6o 

fi^e 

2,65 

12 

13 

12.73 

2,70 

1.2,70   2,76 

12.69 

2,81 

i2,68 

2,87 

13 

*4 

13.69    2,91 

13,63   2.97 

13,67 

3,03 

I3,6,5 

3-°S 

14 

15 

14,67 

3.12 

14,66   3.18 

14,64 

3,25 

14.63 

3:31 

i  5 

1  6 

15,65 

3,33 

15.64 

3>39 

15,62 

3>46 

J5.6i 

3,5? 

16 

17    16.63 

3,53 

16,61 

8.** 

16,60! 

3,68 

*6^j 

3,7,r 

17 

18   17,61 

3,74 

17,59 

3,82 

17,57 

3?9° 

J7,56 

3»97 

18 

19   18,58 

8,95 

18,57 

4,°3 

18,55 

4,11 

18.53 

4-I'y 

i.9 

.  20 

19,50 

4,16 

19,5-1    4<24 

I9-C3 

19-5  l 

4,41 

20 

41 

20,54 

1737 

20,52 

4,46 

20,50 

4  55 

20.48 

4-6? 

2  1 

22 

21,52 

4,57 

21,50 

4^67 

4.70 

21,46 

4,86 

22 

23 

22,50 

4,78 

22,48 

4,88 

22,45' 

4,98 

22,43 

23 

24 

23,48 

4,99 

23,45 

5,09 

23,43' 

5,J9 

23,41 

5,3r 

24 

25 

24.45 

5.20 

24,43 

5:3° 

24,41 

5.41 

24.38 

5.52 

25 

26 

25,43 

5»4* 

25,41 

5,52 

25,38 

5=63 

25.36 

5,74 

26 

27 

26.41 

556i 

26,33 

5»73 

26.36 

5,84 

26,33 

5.96 

27 

28 

27.39 

5,82 

27.36 

5,94 

2  7,  34 

6,ob 

63i8 

28 

29 

28,37 

6,03 

28;34 

6,15 

28,31 

6,a8 

28'aS 

6,40 

29 

go 

29,34 

6,24 

29.31: 

6.  3  7 

29,^9 

6  49 

2,9.  s( 

6,62 

30 

Si 

3°,  3  2 

6.45 

30,29 

6,58 

30,^7 

6,71  i-  3'  -,24 

6.8a 

31,30   6,65 

31,2? 

6,79 

3^24 

6,93 

3i52 

7.06 

3  2 

33 

32,28 

6,86 

32,23 

7,0.0 

32.19 

7,28 

33    I 

34 

33,26 

7,07 

33,2.; 

7,21 

33,T9 

7:36 

33,16 

7,50 

34    '1 

35 

34,24 

7,28 

34,2' 

7,43 

54.17 

7,58 

34,  i/ 

7,72 

35 

36 

7,48 

35,  iB 

7,64 

35,15 

7,79 

35,i 

7,95 

36 

37 

-r;6,i9 

7,69 

36,16 

7-85 

8,01 

8,1 

37 

38 

37,17 

7-9° 

37,i'. 

8,06 

37,10 

8,22 

3^,0 

8.3 

38 

39 

38.15 

8,11 

38,11 

8,27 

38,08 

8,44 

38,0 

8,6 

89 

39,13 

8,32 

39.09 

8,49 

'-^05 

1  8  66 

8,8 

-IP. 

4,1 

!<MC 

8,j2 

40,07 

3,7° 

40tcg 

8,87 

-1"»9 

9,°j 

42 

41.08  8.73 

41,04 

89; 

41,00 

9jG9 

41,9 

9.  a 

42 

43 

42,06   8,94 

42,02 

9,22 

42.98 

9?3r 

4^,9 

9.49 

43 

44 

43»°4 

r     9  ,  '  5 

43,  of 

9,34 

43596 

9.52 

43,9 

9^7 

44 

45 

44,05 

9  36 

44,98 

.9,55 

44,93 

9.74 

44,8 

9,9 

45 

46 

>   9.56 

!    45,9, 

9,76 

9^6 

45,8 

46 

47 

46-9: 

'   9-77 

i   46,9. 

9,97 

46^89 

10,17 

10,3" 

47 

48 

>   998 

if  47-9  ' 

to,  18 

47,86 

I0,39 

47  o 

!•''.  5 

48 

49 

48,9! 

!  io;t9|!48,8^ 

fo,4o 

48,84 

10,  61 

48,70 

10,8 

49 

5° 

49  9'1  IO-4C  (i  49il< 

<o.6i 

/i  0   8  < 

10,82  |J  40.7 

II'° 

c: 

Drp.'jjtot.    jj  ^"p.'Lat. 

A)  n. 

c-:  &S 

;Q 

78   Deg.    ii   77  A  Deg. 

77i 

Deg.    Ij  77^  Deg. 

a  8 

T  '  £  *  =-  ^f^  ^f-  -T..-./,-^  '.  •.  r  -  —ST^ssTJliBS^  M 

—  ^arrTu  "  •JSEsrarsEarr'rf:'^''  ^« 

TRAVERSE    TABLE. 


37 

*$D«£ 


Lat.    Deo. 


49,74 

5*',69 

52,67 


54,62 
55'59 
56,57 
57,55| 


11,26 

n',70 
11,92 

12, ,4 
12,36 


12,80 


59,5° 
60,47  i 

6i,45  T 


63,40 
64,37 
65,35 
06,32 

67,3° 

68,2 


14,12 


5,0 


69,25  T5,< 
70,22115,; 
7J,2o|i6,; 
72,iSji6,< 
73,15*6,- 


91,71 
92,68 
93,66 
94,63 
95,6 1 
96,58 

<&53 
£>eo. 


io,77 

16,99 

7»2 

:7-4-, 
17,66 


74,13 

76,08 
77,05 
7^3 
79,00 
So.qS 

8i:95 
82,93 
83,90 

84,88 

85,85 
86,83 
87,81 
.8^,78 19,86  90 


*7,88 
18,10 


^8,76 


5i 
52 
53 
54 
5'5 
56 
57 
58 

59 
60 

61 

62 
63 

r4 
65 

66 
67 

68 
69 
7£ 

72 
^3 
74 
75 
76 
77 
78 

79 
80 

81 

2 

83 
84 

85 
86 
87 
88 
89 


20,08 

20,30 

20,52 

2°,75 
20,97 

21,19 

21,41 
21,63 
21,85 


99 


22,07,00 
Lat.  [^ 


Q  '  7« 

^CS-^ 


ILJCV,     Udl.      1    .--          j< 

77^Deg-1<5    | 

"22* 


28 


TRAVERSt'TABLE. 


iSJv  **"V  iimi            i    r                        ni                 ii     i                       *"'i  i^f^  Sf 

^-  UA 

BW  

1  3  Deg. 

i  -i\  De^-. 

M£  Deg. 

13!   Deg 

5  c 

•V  p 

La1.    Dep. 

D?n 

L^. 

T57p. 

Lat. 

3ep. 

r3  ' 

^7 

0,9 

0,23 

0,9 

O  9.c- 

0.9 

0,23 

0,97 

0,2^ 

i 

r 

1.95 

0.4.5 

1-95 

0,46 

1,9; 

0.47 

1,94 

0,48 

2 

c 

2,92 

0,67 

2,92 

0,69 

2,92 

0,70 

2,91 

0,71 

3 

4 

0,90 

0,92 

3,89 

°'93 

0.95 

4 

c 

l| 

i,l2 

48-7 

l,lj; 

4,86 

4,^86 

1,19 

6 

i,35 

5*84 

1,38 

5,83 

1,40 

5,8c 

1,43 

6 

7 

6*82 

6,81 

l,6o 

6,Si 

1,63 

6,80 

1,66 

7 

8 

7,8 

l,oC) 

7,79 

1,83 

7,78 

1,87 

7,77 

1.90 

8 

9 

8,77 

2,O2 

8,76 

2,oC 

8»75 

2,10 

8,74 

2,14 

9 

10 

9,74 

2,25 

9*?"1 

2,29 

Q-72 

2,33 

9-7T 

2>38 

10 

1  1 

10,72 

2,47 

10,71 

2,52 

10,70 

2,57 

10.68 

2,61 

11 

12 

U369 

2,70 

11,68 

2,75 

11,6? 

2.80 

n,66 

2,85 

12 

13 

2,92 

12,65 

e;98 

12,64 

3.03 

12,63 

3»°9 

13 

I3& 

3»J5 

13,63 

3,21 

13,61 

8,27 

13,60 

3,33 

14 

15 

4,6z 

3.37 

14,60 

3^44 

14,59 

3  550 

14^57 

3,^7 

15 

16 

15,59 

3,6.) 

15,55 

3-6; 

15,56 

#>74 

15,54 

3,80 

16 

*7 

16,57 

3,82 

16,55 

3>9° 

1^,53 

3*97 

16,51 

4,04 

17 

18 

',54 

17,51 

4,13 

17,50 

4,20 

17,48 

4,28 

18 

19 

1851 

4?,27 

18,49 

4,35 

18,48 

4,44 

18,46 

4,52 

19 

oo 

19,49 

19,47 

4,58 

19,4' 

4.67 

19,43 

4,^5 

20 

El 

20,46 

4,72 

20544 

4,81 

20,42 

4,9J 

20.40 

4,99 

21 

S2 

2I:44 

4,95 

21,41 

5,04 

2i,39 

5.14 

2i>37 

5.2^ 

22 

23 

22,41 

5,17 

22,39 

5,27 

2  2  ,  3  '-j 

5,37 

22.34 

5,47 

2.Q 

24 

^•38 
24,36 

5,4° 

?,O2 

24^3 

5,5° 
5»73 

24.31 

5,&l 

2.^28 

5>7° 
5,94 

24 
25 

26 

^5,33 

5-85 

25,3' 

5,96 

25,28 

6,07 

6,  1  8 

26 

27 

26,31 

6,07 

26,28 

6,19 

26,25 

6,30 

26,23 

6,42 

27 

28 

6,cfo 

27,25 

6,42 

27,23 

6,54 

27,2 

6,66 

28 

29 

28^26 

6  52 

28,23 

6,65 

28,20 

6,77 

28,17 

6,89 

22 

6,75 

S»<),2< 

6.88 

29,  V? 

7  oo 

20,14 

7,13 

3° 

31 

0,21 

6,97 

30'1/ 

7.11 

30,14 

7,24 

30,11 

7,37 

3* 

31.18 

7,20 

3M5 

7,33 

3^12 

7?47 

31,08 

7,61 

32 

33 

2,15 

7,42 

32,12 

7,56 

32,09 

7,7° 

32.05 

7,84 

33 

34 

33,13 

7,65 

33,  oq 

7,79 

33-06 

7,94 

33,°3 

8,08 

34 

35 

4,10 

7,87 

34,o8 

8,02 

34,°3 

8,17 

34,00 

8,32 

35 

5,o8 

8,10 

35,04 

8,25 

35,01 

8.40 

35,07 

8.56 

36 

37 

6,05 

8,32 

36,02 

8,48 

36,98 

8.64 

36,94 

8,79 

37 

38 

7,°3 

8,55 

37,99 

8,71 

37-95 

8,  '87 

37,91 

9,03 

38 

39 

8,oc 

8-77 

38,96 

8,94 

38,92 

9>I<> 

38,88 

9,27 

39 

II 

9.97 

9  -°\ 

39,94 

9-17 

39.8o 

9  »34 

39,8? 

9,51 

40 

41 

0,95 

40.91 

9.4° 

4->,87 

9,57 

4^,83 

9,75 

41 

42 

1,92 

9,45 

41,88 

9-63 

41.84 

9,80 

41.80 

42 

43 

2,90 

42.86 

9.86 

42,81 

0,04 

42^77 

O.22 

43 

44 

3;87 

9,90 

43,83 

0,08 

43,78 

10,27 

43,74 

0,46 

44 

45 

4,85 

0,12 

44,80 

0,31 

44,76 

10,51 

44,7i 

0.70 

45 

46 

°,35 

0>54 

45,73 

10,74 

45,68 

0,93 

46 

47 

i'so 

0.57 

46.75 

°,77 

46,70 

io;97 

46,65 

1,17 

47 

48 

7,77 

0,80 

47,72 

1.00 

47,67 

H,2I 

46,62 

1,41 

48 

49 

8,74 

1,02 

48,70 

1,23 

48,65 

11,44 

47,60 

1,65 

49 

5r' 

9,72 

1,21? 

49,6/ 

1.46 

49,62 

11,67 

48.57 

1.88 

5° 

&  q 

Dep. 

77    1 

% 

D-p. 

%l 

ijr 

Lar, 
Deg. 

Dep.lLat. 

1    & 

29 


i  H 


TRAVERSE    TABLE. 


c>.uw—  —  --  

4  O     14  Deg.    K!  14!  Deg. 

'4  -J  l>g.  ||     14?    Z**. 

*§j(JVr 

a  py 

r3  HTTbep.  (I  EStTDep.  i 

Lat. 

Dt-p-  !!  Lat.  1 

>  > 

5=  $: 

1 

0,97   0*24  ||    0,97   0,25 

0.97 

°>25  11    6,97 

0,25 

i 

2 

1,94'  0,48  (I    1,94   0,49 

1,94 

^93 

2 

3 

2'9li  o  73  [I    2,qij  0,72 

2,90 

°>75 

2,90 

0,76 

3 

4 

3,88   0,07  II    3,88 

o,98j 

8*9? 

IjOO 

387 

i,  02 

4 

5 

4.85j    1,21   I      4,85 

1,23 

4,«4 

1^25 

4.84 

1,2? 

5 

6 

5,82i  1,45       .5,82 

1,48 

5,81 

1,50 

5,80 

6 

7 

6,79;  1.69       6,78 

1,72 

6,78 

6,77 

1,78 

7 

8 

7,76|  >.  94        7,75 

1,97 

7,75 

2.00 

7,74 

2,  "4 

8 

9 

8,73 

2,  3  8  PI    8,72 

2,22 

8,71 

2,25 

8,70 

2,29 

9 

10 

_9.»7-° 

JM_g  |    9/>9 

2,46 

9.68 

9»6y 

'-55 

to 

1  1 

10,67 

2,66  »l  10,66  4,71 

10,65 

2,75 

10,64 

2,8o 

1  1 

12 

11,64 

2,90  ||  11,63   2,95 

11,62 

n,6t 

3.06 

12 

13  J18.6I 

3-15  ij  12,61 

3.20 

12,59 

3,25 

I-j57 

3  31 

13 

H 

3,5* 

3,39 

13j<?7 

3»45 

13,55 

3,51 

T3,54 

3,56 

'4 

15 

4,55 

3,63  | 

14,54    3,69 

14,52 

3,76 

'4-51 

3,82 

£ 

16 

5.52 

3,^7  ' 

1.5-  51 

3,94 

»5»49 

4,0; 

J5'47 

4.  '•! 

10 

»7 

6.50 

4,1  1 

16,48 

16,46 

4,26 

16,44 

4,3? 

J7 

18 

7,47 

4,35 

17.45 

4-43  I 

17-43 

X7.4I 

18 

19 

8=44 

4.60  i 

18,42 

4,68 

18,39 

4,76 

18,37 

4,84 

'9 

20 

9,41 

4.84 

12?!8 

1 

10.36 

5.01 

19.34 

5.0-9 

20 

21 

20,38 

5,08 

20,35 

5,  i?  ]|  20,33   5.  a6 

20,31 

5-H5 

21 

22 

21,35 

5-32 

21.32 

5,49  ,121,30   5,5i 

21,28 

5,6o 

22 

23 

22,32 

5,56 

2?.s2fi 

5,66   |  22,5.7    5,76 

22,24 

5,86 

23 

24 

23.29 

5,8i 

23,26 

5,91  I  2.3,  *4 

6,01 

23,21 

6,11 

24 

24.26 

6,05 

24,23 

6,15  ||  24,20 

6,26 

24,18 

637 

'25 

26 

25,23 

6,29 

2,5,20 

6,4°  I  25,17:  6  51 

25--  M 

6,62 

26 

27 

26,20 

653 

26,17 

6,65!  26,14 

6,76 

26,11 

6,87 

27 

28 

27,17 

6,77 

27,14 

6,89  |l  27,11 

7,01 

27,08 

7-  ^S 

28 

29 

28,14 

7,02 

28.11 

7,14  i 

28,04 

7,3! 

29 

30 

29,11 

29.08 

7,38 

29,04 

7,5' 

29,01 

,7^4 

30 

30,08 

"T^ 

3°>c'5 

^563  |i  30,01     7.76 

29,98 

7,8o 

3» 

32 

3V  5 

7-74 

31,02 

7,88     30,98 

8,01 

00,95 

8,  i 

32  1 

83 

32,  "2 

7.98 

31,98 

Q 

8,26 

3  *  -  9*1 

8.40 

38    ! 

34 

32-99 

8,23 

32,95 

8'37  It  3^92 

8,51 

32,  8S 

8,66 

34    ' 

35 

8,47 

33.92 

8,62     33.89 

8'.;/6 

33»8,r 

8,9 

35 

36 

34*93 

«,7i 

34^9 

8  86      34,85 

9,01 

34  81 

9,17 

36 

37 

8-95 

3C»^^ 

9>Ti  fl  3.?,  82 

9,26 

35-78 

9,42 

37 

38 

36!87 

9,19 

,36,83 

9,35 

36,70 

9.51 

36,75 

9,6 

38 

39 

37-84 

9=44 

37,80 

9,60 

37  76 

9.,76 

37-7 

9,0 

39 

.4°. 

38,81 

9,68 

38.77 

9.85 

II  38,73 

38,68 

10,1 

40 

4j 

39,7^ 

9,92 

39»74 

IO,C9  II  39,6o 

10,27 

39  '6. 

10,4 

41 

42 

4°,  75 

1  0,1  6 

40,71 

10,34 

4>.  66 

10,52 

4,.,62 

iu,6 

42 

43 

4i,72 

10,40 

41,68 

10,58 

41*-6j 

10,77 

10,9 

43 

44 

42.60 

10,64 

42,65 

[0,83 

42,60 

11,02 

42^55 

11,2 

44    | 

45 

43,6610,89 

43,62 

11,08 

43,57 

11,27 

43,5 

11,4 

45    1 

46 

44,58 

11,32 

44,52 

rl^2 

n,7 

46    | 

47 

45,6011,37 

45  55 

11,57 

45  5C 

H577 

4,',  4 

11,9 

47 

48 

46,5711,61 

46.52 

11.82 

46,4; 

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48,4^ 
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75.3  Dc>o-  II    75s    1JeS-  !!  75i  De£- 

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60 
61 
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65 

66 

68 
69 
70 


84 

85 
86 
87 
88 
89 

£1 
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92 
93 

194 
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96 

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100 


14   Deg. 


50.46)12,58 
5«,43IV-2 
^2,4013.06 

53,37 
54,34 
55»3' 
5MSi4»< 

57,2?  14,27 

58,22 

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68.89 
69',  8  6 


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17,06 
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71,80 


73,74 

75^8 

76.65 

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7^,59 

79,5* 

80,53 

01,501 

82^4820,56 

83,4520,81 

84,4221,05 

85,392t'29 
86.3621,53 
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19,35 
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20.    8 


94,1223,47 
95,0923,71 

96, 06  2-). 95 
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76   Deg. 


£T 

49)4? 
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51,37 
52,34 
53, 3! 
54,28 
55-25 

57',!i 

50.12 

60,09 


I  2, 80 

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14,28 


15,02 
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72,69 

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76.57 

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81,42  20 


34,32 


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86. 
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88,20 
89,17 


95,95 
06.92 


18,46 
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19,69 
19,94 
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21,17 
21,42 
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22,40 
22,65 
22.80 


91,11 

92,0823 

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24,37 
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49,3«i2,77 

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52,28 

53,25 

54,22 


56,15 

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58,00 


'4,27 
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59,06115,27 
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61,96  16,02 


62.93 


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64,8716,78 

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17.53 
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74,5 


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11,78 


85,3022,03 


86,17 

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90,04123,29 

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92.94  24,04 
03.91  24,29 


94,8824 

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96.81 


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24,79 

25,  "4 

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75  k    Deg' 


f^RD^i 


12,98 

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49,32 
50,29 
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52,22 
53,19 
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80.2621,13  83 

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30,80 

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31.88 

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31,8; 

8.68 

31,80 

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10,26 

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46.25 

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47,33 

12,68 

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75    Deg. 

74i 

74-J-  Deg. 

T  R  A  V  E  R  S  E     T  A  B 


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15  Deg. 


La-. 

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525<>,23 
51,19 


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58 , 56,021 5,0 1 


59 


13,20 
13,46 

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49,I5|i3  63 
50,  MI  3. 90 
51,07  14,16 
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53-ooji4,7o 
53-96  M4597 
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58,8^16,04 
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60.7816,57 


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13,68 
13,94 

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53,06^4,47 

54»°3!14,73 
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7572.44; 
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20,45 

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8(983:67i*M6 


8885,01 
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91  ,'87.9  •»3:-55 
92(88. 87J23,8i 


93:89- 


9692.73  24,85 
9793-6 
9894,6 
999/j£ 


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24.33 


25.61 


62.71 
63,68 
64,64 
65,61 

66,57 

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68:<5o  ts,68 


69,46 


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71.39 


16,83 
17,10 

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17,62 

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19, 4< 


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74,2920,2? 
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58;78j»",-3" 

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6  ,-iji6,84 

6i,67-»7'.io 


63,60117,64 
64.5617.9° 

65,33  l8;17 
66,4918,44 
67,4y|l8,7I 

68,42518,97 

6  A,38j  19, 44 

7«,3i|'9'78 
72,27120,.  4 


20,58 


79,n*i,57 

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82.97122,62  || 
83,94|22,8S  I! 

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86,8  afcy^ 
87,80^23,94 

88.76  24.20 
89.7324,46, 

9  ',69^24,72  j 
91,65124,99 

93^825^1 

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76,13.21,11 

77v99|2i»38 
78,0^21,6,5 
79,0^121,91 


80,94 

82,87 

83>8 
84,8 

85,76 

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22.72 
22,98 


23,78 

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25,39 
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49.00 


51,9; 


539ol5 


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60,6 
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63,5 
64,4; 

65,4 
67,?; 

68,3.' 

69,30 

70,2 

71.22 

72,18 


77-96 
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81,81 

8^73 
84,70 
85,66 
86.62 
87;58 
8»,55 
89.51 
9o,47 
91,43 
92,40 


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4,16 

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4 
5,  a  4 

5,52 

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15,05  i|  92,40     0,01 

?-5-9*  jj  93  36q6;33 

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26,72  jj  §6,25 
L,r"  I?  Dep, 
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53 
5-1 
35 
56 

li 
6t 


64 

65 
66 
67 
68 
60 

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72 

73 

74 

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77 
7« 


TRAVERS 


q  u 
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TRAVERSE    TABLE. 


53 
54 

5£ 
56 

57 
58 

59 
60 

•61 
62 

63 

6,4 
65 

66 

67 
68 

69 

22 

71 

72 

73 
74 
75 
76 
77 
78 

7.9 
80 

81 
82 

83 
84 

85 
86 

87 
88 

89 

9_1 

92 
93 
94 
95 
96 

97. 
98 
99 

100 


?y 


-  ..  16,26 
57,68  J6,54 
58,64  16, 81 
39,60  17,09 

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61,52  17,64 
62,48  17,92 
63, 44  TO  T« 

64,4°  *o,i7 
65,37T8,74 


§7,_2.9 

68, 

69,21 

70,17 


73,06 
74.02 
74^98 
75,94 

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lill? 
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19,85 

20,12 
20,40 
567 


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77, 
78,89 

79,78 


21.22 


00  22 


8622 


21.78 
05 


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22^88 


8  ',  7  '23,43 
82,6723,70 
83,6323,98 
84,5924,26 

85,5524,53 
86,51  24.81 

87,47  25,08 
88,44  25,36 

89,4°25/>3 

9°j36»5»9J 

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^,,826.46 
93,2426,74 
94,2027,01 
-  ,1627,29 


Dep.  far 


74 


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68,i6I9-87 
69,12  20,15 
7^,0820,43 
71,04 

72,00  ,7y 
72,9621,27 

73,92  2T ,55 
74.8821,83 
75,8422,11 
76  8022,39 
77,7622,67 


79 
80,64 

81, 
82. 


6823 


60-23,7 


5624-,o7 


«3»52 
84,48 

85-44 

g6  40 

87,36 
88,32 
89,28 

91,20 

92,16 

94,08 
96.00 


23,5! 
3,79 
7 

24,35 
24,62 
24.90 


26,02 
26.30 
2658 
26,86 

27, H 
27,42 
37,70 
12Y9_8 
ar.. 


16%  Deg. 
Lar,  Dep. 
48,9-  T^ 
49,^  .4,77 
50,82 

>5-.d4 
15,61 


16,76 

1 7,°4 


54,65 
55, 61 

56,57 

58^9 
59--45 
60,41 

61,36 
62,32 
63,28 
64,24 

66,^6 

68^8 
69,03 
^9,99 
70.95 

72?87 

73,83 


76.71 
77.66 
78,62 
79,58 

8i!$o 
82,46 
83.42 

84,38 

85*33 
86.20 


88.2. 
89,17 
9M3 


93»96 
95,88 


17,61 

ih%i8 
18,46 


19;3* 
i9,1*S 


20,45 
20,73 


21, ?9 

--•    7 


2,72 
3,01 


3,57 
3,86 
4.14 

4,43 

24,90 


25,85 
6,13 
6.41 
6,^70 
6,98 
7,27 
7;55 
7,83 

8.12 

8.40 

.ll-at. 


LH       Ueo. 


48,84 


99 

:?ri5,'7 


52,67 


54,5816, 


I5,56 
16,14 


56.5- 

57-45 

58,41 

59,37 

60|33 

61,28 

62,24    -Jf0 

63,9019,0^ 

64%i6|'9,3i 


17,00 

.20 


i  •>-•  I 

18,15 


6V,  1 1  19,60 


66,07 

67,00 


19.89 
20, 17 

67,99120.46 
68,05:20,75 
69,9°i2i504 
70,86121, 


?2lj90 


74.69522,48 


!C 


?6/>i 


*7  * 
5  /  / 


82 
83 


78,5*|23,63 
79  =  4823,92 
80,4424,21! 
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-,35M'78  8 


83,3t|25>07' 
81,2725,36 
„.  \*S*65 
86;t8! 

87,14 
82  10 


06,23 
26,'8o 


90,01 


91.93 


92.88 


87 
88 

89 

91 

92 

93 

94 
-   ,  95 

27,67,  96 


27,91  97 
28,24!  98 

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23,8g|,oo 

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TRAVERSE     T    A  B  I,  E. 


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Sr 

Deo. 

17!  Peg. 

"WjJ  iJ 

.1 

Dep, 

Lat. 

i 

°,9< 

>    o,«9 

o,9s 

0.30 

0.9  ; 

0,3  ; 

0,9! 

i  0^3, 

l 

2 

1.9 

o  5^ 

1.01 

°»^9 

1,91 

o.6j 

1,9^ 

>   0,61 

2 

3 

2,8; 

0,83 

2,87 

0,89 

2,8c 

0,9  ^ 

2}8 

0.91 

3 

4 

3,8. 

1,17 

3-32 

1,19 

3,8i 

1,20 

3.8 

1,22 

4 

5 

4,7* 

1.46 

4.7^ 

1,48 

4,77 

1,50 

4,7 

1,<52 

5 

6 

5,74 

1,75 

5-73 

1,78 

5*7* 

,1,8.) 

5,7 

1,83 

6 

7 

6.69 

2,05 

6,69 

2,08 

6,6b 

2,  to 

6,6 

2>  1  c 

7 

8 

7,6c 

2,34 

7,64 

2.37 

7,^i 

2.41 

7,62 

3>44 

8 

9 

8,61 

2,63 

8.6-: 

2,67 

8,58 

2,71 

8,57 

2,  7  A 

9 

10 

9,56 

2.V2 

9*5.5 

OyCj 

3.QT 

9-.5 

3-"5 

10 

1  1 

io,5 

3,22 

"3,26 

io,49 

3,3  ' 

10.48 

1  1 

12 

11,48 

3.5  l 

i»  ,'46 

1  1'4:t 

8-6  1 

11*43 

3$6 

12 

13 

12,43 

12,42 

3*85 

12,40 

3^91 

1:2,38 

3»96 

13 

13-39 

4,°9 

'3,37 

1  3*3,5 

4,21 

13,33 

4,27 

14 

15 

M,34 

4,39 

14,33 

4>45 

14,31 

4,51 

14,^9 

4»57 

1  5 

16 

15,29 

4,t8 

1,5,28 

4,74 

15,26 

4,81 

15,^4 

4,88 

16 

i  7 

16,26 

4'97 

16,24 

16,21 

16,15 

<;,i£ 

17 

18 

17,21 

5,26 

17,  it, 

5,34 

17,17 

5-4« 

17,1' 

5»4.9 

18 

19 

18,17 

5,56 

18,15 

5,6,3 

18,10 

18,10 

5s  79 

1  9 

20 

19;T3 

5*85 

19,  i' 

5  -93 

195,17 

6,01 

J9,°.r 

6,10 

20 

ei 

20,  -8 

6,14 

2-t.e/> 

6.13 

aa,p3 

6,3  f 

2.),  00 

6,4" 

21 

22 

2l,°4 

6,43 

21,0) 

6.52 

30.98 

6,62 

20,95 

6,71 

22 

23 

21,99 

6,7* 

2.1,97 

6,82 

^1,94 

6,92 

219 

7,0.1 

R3 

24 

22  95 

7.02 

22,  9^ 

7,12 

32,8^ 

7  2?. 

22,86 

7  ,  0  2 

"4 

25 

23.91 

7,01 

23,88 

23.84 

7,52 

23,81 

7.62 

25 

26 

24,86 

7,6- 

24,83 

7,71 

24,8 

7.82 

24,76 

7  -93 

£6 

27 

25,82 

7  '89 

25,79 

8,01 

25,75 

8,12 

8,23 

27 

28 

26,7? 

8.19 

26,74 

8,30 

a  6,  7 

8,42 

26,67 

8,54 

28 

29 

*7,7^ 

8,4-5 

8,6, 

27,66 

8,71 

27.62 

8,84 

2.9 

00 

28,6.9 

.1-iZI 

28^65 

28.6, 

O    ">2 

9  15 

QO 

(JL— 

31 

29,65 

9.06 

29,61 

~<M9 

29,57 

~'~i'»  ' 

""        ~  —  - 

.9  '45 

31 

3* 

30.60 

9,36 

.949 

3°'5S 

9^64 

30,48 

32 

33 

31,56 

9,65 

3  1'52 

3*>47 

9,92 

31  4,'-< 

1  0,0  6 

33 

34 

32,51 

9-94 

32,47 

10,08 

32  ,2 

10,2^ 

32,38 

«-;37 

34 

35 

33,47 

10,23 

33:4;- 

10,38 

:  c  ,  5  "  ' 

33-33 

10,67 

35 

36 

34,4; 

0,53 

34,32 

10,68 

34?33 

10,83 

34.  *9 

10,98 

36 

35,33 

io,8^ 

35-34 

10,97 

35.2Q 

1  1,  '  3 

11,28 

37 

3': 

36,34 

11,1.1 

36,29 

n.,x7| 

JIJ43 

3^>  IV 

11,58 

38 

39 

37-3° 

11,40 

3  '"•  -  'j 

37.15 

1  1  .  7  '^ 

37>l4 

11,89 

39 

4_ 

38,25 

11,69 

38,40 

u!sc 

I  :?  •  O  '-* 

3?>i0 

12LL9_ 

4° 

39,21 

i1,  99 

397To 

12,  l6 

tatsa 

12,  <C 

4i 

42 

40,16 

i2fa8 

4*>,lJ 

12,45 

•i,*0' 

r»;6i 

4*>,o 

42 

43 

[1,12 

I2>57 

41,07 

12,75 

-j't  ,  ) 

12,9  , 

10.95 

13,11 

43 

44 

:2,0^ 

t*,86 

42,  op 

13,-^ 

t3-4 

4*991 

3>4* 

44 

45 

:3-°3 

18,16 

42,91- 

I3;34 

42,9; 

42,86 

13,72 

45 

s* 

46 

43'99 

3,45 

43,9,- 

'3'6.t 

i3>^} 

43>8> 

14-02 

46 

47 

•4?95 

'3,74 

44,^0: 

13,94 

'4>  13 

44,  7^ 

4-33 

47 

o 

48 

45,9° 

45,84 

14,*3 

4;    7' 

'4-43 

4>",7' 

48 

49 

0,'  6 

r4?33 

46.  8c 

14,53 

46,   ;. 

'  1  73 

46,67 

4,94 

49 

•52. 

:7^ 

i4L6_z 

47-7." 

47^^ 

3>-  -1  : 

-2ll. 

£i 

7s~i 

Lat, 

D;p. 

^il: 

7-2'      J 

— 

'^ 

72l-  J 

%&$ 


T  RAVE  R  S  E    T  A  B  L  F. 


=^#D: 


q  >7 


91187,0226,61 
9287  9826,90 
938804 
9489,89 


97 


lex 

L% 

&£    73~"Deg. 

^^ 


TRAVERSE    T  A  B  L 


18 


49, 45  * 6, 07 


50,41 
5  i  ,36 
52,31 
53,26 

55, l6 


58, oj 
5^,97 

60,87 
6 1,8* 
62,77 

64,67 
fi£j7 


68,48 


72, -28 

74MF 

75,»  3 
76,08 


77,04 
77,99 


»4   79,% 


85 

86 


80,84 

81.79 


6.38 
16,69 
17,00 

17,61 
17,92 


8 


4«.43  '5,97 
49.38  16,28 
5o',33|i6,6o 

52,23|r7,22.. 

53, it1 


0,09 
so,  40 

20.70 

•>  i .  a  r    i 


5,°8 

18,48 

,56,98  f B./Q 
19,10 
i9,42 

j  60,7^,04 
6i,732°>36 
6a,6<< 


S-===S=^==M5~^j^  3 < 

Dk'g.   ji  16'   Dc->r.     cTii 


Lat,_jDejp.  fi  Laf .    L>epj 
^l;j|  PI5[16?3^ 

17,13 


1.9»3J 

^0,26 


j  63,63  20,98 


-?^;ij.  ^^Sp1^' 

21,63      66,4%,92 


67,43 
2M5.1I  68,38 

79-^33 


72,lP 


23,79 

24,41 

24,72 


15^96,-J 

2.'-,:^  i 


-7 


22,23 

22,55 

2  3,' 7 
^3,49 


73.o«21;43 
Mr74 


25,37 
25/68 


88 

."1118  5-1° 

92 
93 

9s  . 

',;^29,{)7 

97  192,25  29,97  Jj  92,12 

98  iy3   2,    3  ',28  JJ93tc7 

99  ;94,'J 


7^93 
77,^:x; 
78,83 
70,7')  26,31 
^       '  I  r  c  ^ 

C'>?  -2J2O.O2 
8l,67 
82,6!2 
83,57 


ft9  3^  E{  9", 22 


47.56 


«V^7  28,18 

87.^37^,81 

'"':9,i2 
39-44 
-9,75 
30,06 
30,38 


«i» 


3 ".oo  4.'  04. -07 
1  at. 

Beg. 


7'J 


53, 1* 

545°5 

55,5« 


17>7.7 
18,09 
^8,40 

I9»04 


19,67 

'9,99 
60,69  2C; 3, 

62,5920,94 
63,54 


21,89 


-3 


•^6,38 


52,08,17,6^ 


7(',i^3,4S 

7V724',  12 
73,02'~ 

73,97 

74'92J5,'  7 
25-3'-> 


77, 76 

2X34 
79,^626,65 
80,61  26,97 
--  27.29 
82,5- 

27-92 

84,40-20,24 


Ho.  3 


'!-9-5; 


;;,^ 
yijO-i  10.46 

3o,73 


:,4i 


57,7^29,^1 

59,6620,25 
6o,6oieos57 


62,50-21,^2 
635442I?54 


5' 
52 

53 
54 

55 


65 
66 

6  7 


'        xf !  I 

5, -3 4  2 1, 18   69    j 


66,29  ^,50 
67,2322,82 

68,  iS  2 ;;,  i  > 


7f  .02 


7^9^4:75 


7^ 


73,8625,07   ?,> 

76^20,04!^' 
77.65^6,361  H2    I 


?*«?,S  li  i 


f^82^ 
H^irj^^ o  91 


Dc-p. 


CE 


7iJ-Deg. 


89,01:30,2: 
89^96  3C>54:  0,5 
jo,9i(CV,- 

'Si  97 


75  3M 

/-      I  «  ,,      .    ,  ' 


7i-V  DegJo  ;Q 
=^WW4«^ 


SE     TABLE. 


TRAVERSE    TABLE. 


T    R  A  V  E  R  S  E    TABLE. 


/      T&T 

20  Deg. 

20i  Deg. 

20    -| 

Deg. 

20?  Deg/  0£1 

P 

Lar.    Dep. 

L*t, 

Dep. 

Lar.  iDep. 

Lat.    !)eo 

K3    li 

i 

0,94   0.34 

0,94 

°,85 

0.94 

°,35 

c,94 

0 

1 

2 

1,88   0,68 

1,88 

0,69 

1,87 

0,70 

1,87 

0,71 

2 

3 

2,82    1,03 

2,81 

1,04 

2,81 

',05 

2,81 

i,  6 

3 

4 

3,76    1,37 

3,75 

»,33 

3,75 

374 

1,42 

4 

5 

4.70;  1,71 

4,^9 

»,73 

4,68 

*>75 

1,77 

5 

6 

5,64:  2,05 

5  63 

2,08 

2,10 

5  4j 

2,iq 

6 

7 

6,58   a,39 

6,57 

2,42 

6^56 

2,45 

6,'5< 

*  *  o 

2,48 

8 

7,52    2,74 

7,51 

*»77 

7,49 

2,80 

7,48 

2.83 

8 

9 

8,46:   3,08 

8,44 

3.12 

8,43 

3,15 

8,42 

3-19 

9 

10 

9,40^3,42 

9.38 

3<4" 

9.37 

3,50 

3  54 

10 

1  i 

10,34'   3,76 

10,32 

3,8i 

10,30 

3,85 

10.29 

3,9° 

1  1 

12 

11.28   4,10 

11,26 

4,i5 

11,24 

4,20 

JI,22 

4,25 

12 

13 

i2.az]  4,45 

12,20 

45" 

12,18 

4>55 

u  ,  I  u 

4.61 

13 

H 

'3,16,  4,79 

13,13 

4,85 

13,  J* 

49° 

4,96 

14 

15 

I4,i°|  5,J3 

14,07 

5,19 

14)05, 

5,25 

14,03 

5,31 

15 

l6 

!5,04!  5,47 

15,01 

5,54 

14-99 

5  60 

14,96 

5,67 

1-6 

17 

I5:97,  5,8i 

15,95 

5,88 

15,92 

5:95 

15-9° 

6,02 

17 

18 

16.91    6,16 

16,89 

6,23 

16.86 

6,30 

!6.83 

6,38 

18 

19 

17,851  6,50 

17.83 

6,58 

17,80 

665 

17-77 

6,73 

19 

2O 

18,79    6,84 

18,76 

6,92 

18,73 

7,00 

18,70 

7.09 

20 

21 

J9,73 

7,18 

19,70 

7  27 

19,67 

7,35 

19.64 

7:44 

21 

22 

20,67 

7,52 

20,64 

7,61 

20,61 

7,7° 

7,7.9 

22 

23 

21,61 

7,87 

21,58 

7,96 

21-54 

8,05 

21,51 

23 

24 

22,55 

8,2! 

22,52 

8,31 

22;48 

8,4" 

22,44 

8^5° 

24 

25 

23-49 

23,45 

8,65 

23,42 

8,76 

8,86 

25 

26 

24,43 

8*89 

9,00 

24,35 

24^31 

9,2i 

26 

27 

25,37 

9,23 

25',33 

9,35 

25,29 

9,46 

25,25 

9,57 

27 

28 

26,31 

9,58 

26,27 

9,69 

£6,23 

9  81 

26,18 

9,92 

c8 

29 

27,25 

9,92 

27,21 

10,04 

27,16 

10,16 

27,12 

10,27 

29 

30 

18,19 

10.26 

28,15 

10,38 

•28,10 

10,51 

28,05 

10,63 

_3P_ 

31 

29,13 

1  0,60 

29,08 

J°,73 

29,04 

10,86 

28,55 

i  .,98 

32 

S'1,0? 

10,94 

30,02 

11.08 

29-97 

11,21 

29,92 

32 

33 

31,01 

11,29 

30,96 

11,42 

30,0,1 

11,56 

30,86 

11^69 

33 

34 

31.95 

11,63 

31,90 

i  T,77 

aw 

H,9I 

31-79 

12.05 

34 

35 

32^,89 

"S97 

32,84 

12.1  1 

32,78 

12.26 

32,73 

12  40 

35 

S6 

33,83 

33,77 

12.46 

33-72 

12,  6l 

33,66 

12,?5 

36 

37 

34,77 

12,65 

34,71 

12,8; 

-4,66 

12,96 

34.60 

'3,n 

37 

38 

13,00 

35,6.5 

•  3.15 

35,59 

13-31 

35,54 

38 

39 

36.65 

36,59 

13,50 

36,53 

13,66 

is',82 

39 

4° 

37-59 

lfj§ 

^53 

111?4 

H'«  i 

37,41 

'4,17 

-1°. 

4i 

38.53 

I4..02 

38,47 

14.19 

SM0 

14,36 

38,34 

'453 

4i 

42 

39,47 

39?40 

14.54 

39,  3  4 

14.71 

39,28 

14,88 

42 

43 

40.41 

14,71 

4°,  34 

14,88 

40,28 

15.06 

40,21 

15,23 

43 

44 

15.05 

41,28 

15,13 

15,41 

15,59 

44 

45 

42,29115,39 

42,22 

15,58 

42,15 

15,76 

42,08 

'5,94 

45 

46 

43,2315,73 

43,i6 

15,92 

43,o9 

16,  1  1 

16,30 

46 

47  |44«'7  16,07 

44,09 

16,27 

44.02 

16.46 

43*95 

16,65 

47 

48 

4^,11^6.42 

45,03 

16,61 

^14,96 

16,8  1 

44,89 

17,01 

48 

49 

46,>--4:j6,76 

45,97 

16,96 

'45,90 

17,16 

17.36 

49 

o 

46.98  17,10 

46,91 

17.31 

46.83 

17-51 

.16.76 

Dep. 

Lat. 

D'p.  Lat. 

IJpp. 

U>.  i.. 

Lat. 

«    ^ 

5      70  Deg. 

69  J  Deg. 

69-^  Deg. 

69-1   Deg, 

a'O 

T  R  A  V  E  H   S  E    T  A  B 


«M3J» 

Si 


5' 
52 
53 

54 
55 
56 
57 
58 
59 

67 
62 

*3 
64 

65 

66 

67 
68 

69 

111 

72 
73 
74 
75 
76 

77 
78 

E 

81 
82 


2oJDeg._  I!    20 l 
Lat.    Pep.  I]    L 


17,79 


50,7418,47 

51,6813,81 

52,62  19,15 

53,56*9,50 

54,5° 

55<44 


0,  1  4 


19,84 
20,18 


20,86 

58,26  21.21 

59,2021,55 


21,89 
22,23 

be, 02122, 57 
62,96  22,92 

63,90 
64,84 

65,78 

16  72 
67,06 
>8,6o 
69,54 
70,48 
71,4-2 
72,36 
73,3° 
74,  M 


76,12 


77,99 


24,28 
24,63 


26.68 
•27,02 
,36 
-27,70 


77,05  28,05 


28,39 


4^.7( 
49,7. 


53,4* 

54  42 

56^ 

58,1? 
59>1] 

60*98 
61,9--' 

62,86 

63,8- 
64'  7* 

66,61 
67,55 
68,4^ 
79,43 

7>'s 
72,24 

73   1 ' 

74,12 


75,99 

7/^87 
78;8i 


0 


18.69 
9^8 


?sL?Si, 

Lat.  I  Dep, 


L  E.  43 

jr^   ^^  ^fr  , 

4     Defr.         C    '$r 


°  5 '  'J  7 

20,42 


22,15 

22;.)0 

7,2,84 

2J,54 


257 


^5,96 
26,30 

26,65 
27,00 
27,34 


28,04 
2  ,38 
28.73 
29,07 
•29,42 


48,71 
49,64 


53,39 
54,33 

5^2< 

58'o7 
,59-° ' 
59 '9? 
6>,38 


18,21 
18,56 
18,91 
19.26 
19,61 
19,96 
20,31 
20,66 

21,01 

21,36 
22,06 

22, 4. 
Z2.76 


64,63 

£*iJ7 

66,50 


23,46 

23,81 


,86 


6^,3^25,57 

25  9'2 
-,2526,27 
26,6, 
72.1220,97 

73, "6  27,32 
74,06 

74,9  ;  ?.?>.   e 

758728,37 
28,7 

9,°7 

78.6829.42 
9,62 


82,43 
83-36 


30,12 
3o,47 
30,82 
3i»i7 


32,22 


86.03  3*,  59;  9- 


87,9033,30!  94 
88  84^3,661  95 
89,77845OIi  9'J 
7'  ;  1,371  97 


5' 

5^ 
-)3 
.54 
5,r, 
5-5 

57 
58 
59 

56_M  2j^26  60 

*7,04ts1^ 


48,63' 1 8,42 


52,3?  *')^\ 
53, yo  20.19 


IJJ  7       tV  >         /          "~f 

60,7^23.03    65 

61,7223,38  66 

62,6523,74!  67 
63,5.9*4,09;  68 
64,52  24,45:  69 
65,4624,801  7£ 

Jft39j*i»»d  71 

68iifc*5»?6  73 

69.2026,22!  7^ 

7^,07  26*32  75 
71,01  27,^8  77 

7-^,94  Z7,63   7« 

73^^27,^9!  79 
74. 8 »  28.35'  sa, 

7j,7528)7°  tNl 
76,68  29, °,V  8,> 
7';,6229;ii:  03 

79'493°,II:  85 
8o,423c?-*7,  8G 

82'293V8|  S8 
83.23  3 ',63^  89 


T  R  A  V  ER 


?>  L  K. 


T  R  A  V  E  R.  S  E    T  A  B  L  E 


31  =c    Des.   II 
SEnKF.ll 


59,55,08  21,14 

6o!56,oi  21, 56 

6^56,9527786 

62J57,88J22,22 
63:58,82  22,58 
64*59,75  22,94 
6560,68.23,29 
6661,621*3,65 
67,62,55  S4,«i 
6863,48,24,37 
6964,42*4,73 

"  35J25>09 


7166, 28*25, 44 
7267,22  25.80 
rn  -  '26,16 


/  O  5  *"J    »»»!«»' 

7469,0826,52 
7570,02;26588 
/670.95a7524 
7771,8927,59 

7872,82*27,95 


8274,69.' 28  ^67 
8i75'6a!a9j03 

8276,5529,39 
8377,49,29,74 
8478,42  30,10 

86,80,2930,82 
8781,22131,18 
8882,1631,54 

89  83,<>9,3  M9 
9_184,  o_a|3BIz.s 

9ij*4,96'32,6i 
92,85,8933,27 
93,86,82  33,33 
9487,7633,69 
95188,6934,04 
96j89,62  34,4 


Lat.  i  Dep. 

I3WI8.4.8 

48;46|i8,85 

5i  526J  i9,'93 
52/1920.30 
53,1220,66 
54,06,21,02 
54,99|2i,38 
55^,21,75 

57,78'22,47 
5^,7222,83 


59,6.5 


23,20 


60,5^23,56 
61,5123,92 
62,44*24,28 
63,38^4,65 
64,3^25,01 
6jk24i25,37 
66,17:25,73 
67,1026,10 


69,9o'27,i8 
70,83,27,55 


73,6328,63 
74.5629.00 

75,49|29,36 
'6.42:09,72 

/7, 3630,08 
78,29130,44 


89,47 


80,15 
81,08 
52,02 

82,95 
8^88 

54,8l 

56^68 
^561 
'8.5434,43 


32,26 
32,62 
32,98 

33,34 


34>°7 


345/9 


61,41124,19 
62,34,24,56 
63,27,24,92 
64,1025.29 

6s .  1 3!2.5166 
66,06:26,02 
66,99^6,39 
67,92^26,75 
68,8.3'27,i2 

6^.78'27?49 
70,71  27.  {% 
71,6428.22 
72,5728,59 
73,5028,95 
74,4329.32 
75536,29.69 
76,293*  05 


78,i 

79,09 

8o,«a 

80.9,5 

81,88 

82,81 


84,67 
85,60 

86-53 
87,46 
88,39 


1,18 


92,11 


30,79 
3i,iJ 


3i, 

32,25 

32,62 

33-35 
33»72 


63,1 

64,° 
65.0 

65,9 
66,8 
67,8. 

69^6! 
7o,5S 

72,'45 
73?35 
74,^ 


75,2^ 
76,10 

77-°S 
78,02 

78,95 
79,8b 
80,81 
8r,74 
82,66 


34'45 
34.82 
895.3235,18 
35,55 


35,92 


854,' 

86,38 

87,3 

88,24 

8-9,  i 

90,09 

91,02 


36.28  S  91,05 


3fv6f  Si  92^8 
.  Lat.    [I  D"eP 


68     Deg. 


24,0 

4-4 
4,8 

^5>2 
55 
W 
'6,3 

;6,6 

7-0 
7,4 
7,7' 
8,1 

8,5 
8,9- 

94 


0,0 

°-7 
J,i 

i',8 

2,2^ 
2,61 
2.98 


4.46 
4,8, 
5,2C 

5,57 
",94 
6-31 
6,69 

,6 

a  . 


45 
'^#D^ 
?.  O  G^ 


53 
54 
55 
56 
57 
5* 
59 
6_I 
61 
62 
63 

fi* 

65 

66 
67 
68 
69 

Z2 

71 
72 
73 
74 
75 
/6 
77 
78 

79 

8  > 

8l 
82 


46 


T    R  AVERSE    TABLE. 


m     .!•....  II.      I      II     I. 

i  22  Deg.    If 


9 
10 

i 1 
ia 
13 

15 
16 

17 
18 


21 
22 

23 
24 

25 
26 

27 
28 
2C) 

3  l 
32 
33 
34 
35 

37 
38 

39 

Jfl 

4' 
42 
43 
44 
45 
46 

n 


°>93   °'37 
1,85'  0.75 

2,78,    1,12 

3«?i    1,50 
4,64    1,87 

5,56,    2,2 

6,49   2,6 
7,42   3,00 
8,34    3,37 


io,a      4>  i  si 


12^05  4,87 

12,98'  5,24 

13.91!  5  62 

I*583|  5,99 

15,76;  6.37 

16.69!  6,74 

17,62  7,12 


2  ,40J   8,24, 

2i>33:  g,6a 
22,25'  8,ocj 

23-18;  9.37 

\*5-°3l°,n 

26,-«9Jio,8j 

fe^i££4 

18,74!  n, 6 1 
-9,67:1 1. 99 

3  ,60!  12. 36 

32,4513,1* 


36.1614,61 


38  94!i.^73 
39.87'  1 6,  ii 
40,80  16-48 
,71.16,86 
42,65 .17,23 

44,50117,98 

i6?36^8,73 

DrpjLat. 

68    Deg. 


6,48 


17-59 
*8,5i    7.  £7 

J9544|  7>95 
2-,36  8,33 
21,29!  8,71 

22,2lJ   9,09 

23,i4i  9  47 

24.06}  9,84 


25,92jio,6 
26,84^0, 98 

28.6911 1.74 


32,39  i 


34,24,14  01 
35,1714,39 
36,10 


16,08 
16,66 


37  95 
38,87 

40,72 
41.65 
42, .57 

44,43 
45,35 


46,2818.9; 


Dep. 


,7,80 
18.18 


'8, 


55 


Lat. 


6,47 


13,86 
H,78, 
15,71 
16.63 


9-95 


26,79  ii,10 

28,6411,86 
29,5612,25 
30,4912,63 


J  32, 34  13-39 
33-26,13,78 
-,4,18  14.16 

36,03:14.92 

36,9615. ;.;i 


=^^ 

Deg. 


67*    fleg. 


39,73 


44.35 
45- 


,6,  7 
16,46 
16,84 
17,22 
17.60 
J7,99 

»8',75 


46,19 
oTTDei. 


Lat. 

0,92 

2,77 
4,6i 

%5l 
6,46 

7,3^ 


T-,v- 

3,83 


18,44 

19.37 
20,29 

21,21 


23.98 
24.90 
25,82 
26,74 
27,67 
28,59 
29,51 
30,43 
31.35 
32,28 

33,2o 
34-^2 

35>97 

3^81 
38,73 
39,  ^5 


42,42 
43,34 

45,  iy 

46 II 

De,. 


Dep 


0  39 
o,77 
i, 16 


2.32 

2, 

3-09 
348 

4J^5 
4.64 

5,03 
5,80 


6,96 
7-35 
7,73 
8,12 
8.51 
8,89 
9,28 
9,67! 

i°!95| 

io,44| 

i   ,83 

U, 2i 
I  1,60 


12,37 
12,76 

13,15 
*3,53 
!3,92 


15,08 

15,86 

16,24 
•6,63 
17.02 
17.40 

'7,79 
18,18 
18,56 

'9,34 
Lat. 


9 

10 

1 1 

12 


16 

17 
18 


20 
27 
22 
23 
24 

26 

27 
28 

29 
31 

3s 
33 
34 
35 
36 
37 
38 
39 

4i 
42 

43 
44 
45 
46 

47 
48 

49 


i& 


TRA 


TABLE. 


TRAVERSE    T  ABLE.             4$ 

^•.WAW 

3  - 

23  Deg.    | 

a^Dejr. 

23^  Dee>  ||    23!  Deg. 

OfJ 

^  ^ 

La-. 

Den 

Lat. 

Dep. 

Lat. 

Dep.  ||  Lat. 

Dep. 

p  * 

v 

46,95 

19,93 

46,86 

20,13 

46,77 

2°,34 

46,68 

°>58 

51 

52 

47,8; 

20,32 

47,78 

2°,  53 

47,6.9 

20,73  I 

47,6o 

5a 

48.79 

20,71 

48,70 

20,92 

48,60 

MS 

48.51 

!>35 

53 

54 

49,7' 

21,10 

49,61 

21,32 

49,52 

»»53 

49,43 

21  '75 

54 

$0,163 

2i,49 

5^,53 

21,71 

5°,44 

l>$3 

5°334 

"2}15 

55 

56 

51,54 

22,88 

51,45 

22,11 

2,33 

51,26 

22,  5^ 

56 

57 

52,47 

22,27 

52,37 

22,CO  1 

52,27 

2-73 

52,17 

22,96 

57 

0 

58 

53,39 

22,66 

53,29 

Z2,go 

53,19 

3,i3 

53,°9 

23,36 

50 

59 

54,3' 

23  05 

54,21 

23,29 

54,1  1 

3,53 

54,°° 

23,76 

£ 

60 

55-23 

23,44 

23.68 

55,02 

3,92 

54*92 

24,  16 

61 

62 

56,15 
57,07 

23,83 

56,05 
56,97 

24,.  8 
24,47 

55*94 
56,86 

24,72 

55,83 
56,75 

24,97 

61 

62 

63 
64 

57,99 
58,91 

24,62 
25,01 

57,88 
58,80 

24,87 
25,26 

57,77 
58,69 

25,12 
25.52 

57,6o 
58,58 

^5,37 
25,78 

64 

f\  r 

65 
66 

59,83 
60,75 

25,40 

25.70 

59,72 
60,64 

25,66 
26,05 

59,6i 

26,32 

60,41 

26,18 
26,58 

65 

66 

c 

67 

61,6726,18 

61,56126,45 

61,44 

26,72 

6i,33 

26,98 

07 

68 
6p 

62,?9  26,57 
63.51  26,06 

62.48 
63,40 

26,84 

27,24 

62,36 
63,28 

27,11 

27,51 

62,24 
63,16 

27.39 
27,79 

69 

64.44 

27,35 

64,32 

27,63 

64,19 

27,9' 

64,07 

28.19 

71 

65,36 

27,74 

65,23 

28,03 

63,11 

28.31 

64,99 

28,59 

71 

72 

66,28 

28,13 

66,15 

28,42 

66,03 

98,71 

65,90 

29,00 

72 

73 

67,20 

28,52 

67,07 

e8,8a 

66,95 

29,11 

66,82 

29,40 

73 

74 

68,12 

5.8.0  1 

67,99 

29,21 

67,86 

29,51 

67,73 

29,8; 

74 

75 
76 

69,°4  29,30 
69,96120.,  70 

68,91 
69,83 

29,6l 

3o,oo 

68,78 
69.70 

29.91 

68,6s 
69,^6 

75 

76 

77 

70.88 

30.09 

7°,75 

3°»4° 

70,61 

30,70 

7°,48 

3l,oi 

77 

o 

78 

71,80 

30,48 

71,67 

30,79 

7i,53 

3!,i° 

7i,39 

31,4! 

78 

79 

72,72 

72,58 

31*18 

72,45 

31,5° 

72,31 

U,82 

79    1 

80 

73,64 

31*26 

73,50 

31,58 

73,36 

31,90 

73,2* 

32,22 

5? 

81 

74,56 

31,65  1 

74,42 

3*>97 

74,28 

32,3° 

74>!4 

^2,62 

81 
8_ 

82 

75,48 

32,04 

75,34 

32,37 

75,20 

32,7® 

75,°6 

33,03 

83 

76,40 

32,43 

76.2.6 

32,76 

76,12 

33'  10 

75*97 

33,43 

R 

84 

77,32 

3282 

77,i8 

&3>i6 

77,°3 

33  49 

76,8.9 

.53,83 

o  _ 

8.5 

78,24 

33*el 

78,10 

33<55 

77,95 

77?8  ' 

'U,93 

05 

0/~ 

86 

79,16 

33,60 

79,02 

33*95 

78,87 

34,29 

78,72 

34,64 

O- 

7 

80,08 

33>99 

79,93 

34*34 

34^9 

79,63 

07 

00 

88 

81,00 

34,38 

80,85 

34,74 

80.  7. 

35*°9 

80,55 

35,44 

QQ 

«9 

34,78 

8i,77 

35,13 

81,62 

35»49 

8i,4< 

3<,84 

oy 

91(82,85 

82,69 

35,53 

82,54 

35,89 

82,3^ 

36,25 

2£ 

9i 

83,77 

35,56 

83,61 

35,92 

83,45 

36,29 

83,2.9 

36,65 

o  <? 

92 

84,69 

35.95 

84,53 

36,32 

84,37 

36,63 

84,21 

37,°5 

y  * 

8,5,61 

36.34 

8  {,45 

36,71 

85,29 

37,08 

85,12 

37,46 

Q 

94 

86,53 

36,73 

86,37 

37,11 

86,ac 

86,04 

37,86 

Qr 

96 

87,45 

37,12 

87,29 

37,5° 

87,12 

3788 

86,95 

38,26 

Q6 

9< 

88,87 

88,20 

37-9° 

88,04 

3^28 

87,87 

48,66 

Q7 

97 

89,  2c; 

37,90 

89,12 

38,29 

88,9; 

38,68 

82.79 

39*°7 

Q8 

9'f 

90,2, 

38,29 

90,04 

38,68 

89,87 

39.08 

89,7^ 

39'47 

99 

ifj 

91,  4 

38,68 

9o,9( 

39^°8 

90,79 

39,48 

90,62 

39,*7 

I  GO 

loc 

92,05 

39,07 

qi,8?< 

39-47 

91,7 

39,87 

91,5 

40,27 

;  «! 

Dep 

Lu, 

Dep 

Lat. 

Dep.'Lat. 

Dep 

Lat» 

»  & 

5  Q    67   Deg, 

66}  Deg. 

66i  Deg. 

66i  Dee. 

a  L 

<o 


it  ^£Pi.L^ni 
i  ^rueg.jj 


65  i  Deg. 


Lat. 

3ep    _ 

0,91 

0.42 

1,82 

0,84 

2,72 

1,2(3 

3>63 

1,67 

4,54 

2,09 

5,45 

2,51 

6,36 

7,27 

3^35 

8,17 

3,77 

9,08 

4>1Q  - 

9,99 

4^61 

10,90 

5>°* 

!i,8i 

5,44 

I2,71 

5,86 

I3,62 

6,20 

14,53 

6,70 

15,4^ 

7.12 

*6j3.5 

7,54 

IM6 

7,95 

19,07 

8,7v 

19.98 

9,21 

20,89 

9,63 

21,80 

0,05 

22,70 

10,47 

23.6 

10,89 

25,43 

Il',72 

26,3. 

12,14 

27.2^ 

12,56 

28,1 

12.98 

29,0 

13,40 

29,9 

13,82 

30,8 

14,^3 

31-7 

14.65 

34»5 

1  5>49 
1^,91 

35^4 

i6,33 

37,2 

1^.76 

38,1 

17,58 

39>° 

1  8,00 

39>9 

18,42 

40,8 

18,84 

19,26 

4^6 

19,68 

43,5 

20,10 

4455 

^0,5  i 

45»4 

20,93 

II  De^ 

Ut. 

[]  "6lfl^g- 

-o'- 
Cr 


9 
to 

1 1 

12 
13 
14 
15 
16 

18 

19 
20 

21 
22 

23 

£4 

25 
26 

07 
28 
29 

-22 

33 
33 
34 

36 
37 
38 
39 


42 
43 

41 

45. 

46 

47 

48 

49 

.52 


TRAVERSE       TAB  L  E. 


24 


Deg.    II    24t    Peg 


Lat.  i  Oep. 
46759 


47,5° 
48,42 


50,24 


51.1622,78 
52,07 
52,99  23,59 


55-73 


5' 

53 

54 

55 

56 

57 

53 

59 

60. 

61 

63 

^4 
65 

66 

67 

68 

69 


71  64,86 

72  65,78 


21,56 
[,96 

22,37 


73 
74 

76 

P 

79 


86 


6,69 

7,6o 

8,5* 

>43 

1,26 
2,17 
3,°  K 
4,0, 
4<9 

6,74 
77,6 
78,5 

Boi3< 
8i,3 


93 
94 
95 
(>6 

97 

98 

99 
atS 

V- 
30 


88,6 


SHE 

66 


6,03 
6.44 
',84 

7',66 
8,06 

!dz 

8,88 
9,28 

0,10 
0,51 

o,9i 


Ml 

s'ss 
3,76 

M,J7 

14,98 

55'39 

}6,20 

36,61 

,7,01 
37,42 
37,83 
38,23 

39^5 
39,4J 
39,80 

40.2? 
40,67 


Lat. 


47,4* 

48,32 

49*24 


52,88 

54 
55,6^ 

5?»44 
58,3: 
59>2 

6V< 

62,9 


l)eg. 
Deo. 


1,36 

'-77 
2,18 

2,59 
asU1 

2<b23 


25,83 
26,29 
26.70 


27,93 


64,7 
65,6 
66,5 

6?,4;; 
68,38 

79, 29 
70,21 

71,12 


72,94 
73,85 
74.76 
75/2 

76,59 
77,5« 

79,3£ 
80,^ 

8i,i« 

82^ 
83.8^ 

840 

86*6 

88,4 

89 ',3 

91,1 


29,16 

29,57 
9,98 

°;39 


0,80 


2,86 


24 


24l  Dep. 


46,41 

47,32 

48,23 

49;l-i 
50,96 

5^,78 

53,69  Z4'47 

i- .  f,"  i 


Dep.  (J  Lat.  rDcp. 


(K 


48,13121, 19 

49, 04! -2, 61 

5'>',8o|23',44 

^CjG/o^^B 
53.58J24 


3,68 

54.509 

Ha  9-1 

55  r  3- 
35,73 

36.55 

36,96 

W,38 
37,79 

^t<,'>.0 

^8,61 

49,02 

39,43 
39,84 

49*66 

41,07 


Dcp.  Lat. 
65|'De^ 


55,  5  » 


,8,24 
59, 1 5 


>'J  I  ny 

hf^!*5^£J   6> 

5>4')|a5>54   67 


55 


26,13     57,2i;20,3 
26, 54  11  58,12:26,79 
^6,96. 


Pi 

52 
53 
54 

56 


58 

59 


6o,o6|27,37  j!  59,94^7,^3 
6^,97  27.78  I  60,8528,05 
61,88  28^0 
62,7928,61 


62 

P 

65 
66 

67 
68 

69 

70 


65,52j29.^6 
66,43:30,27 
67;34Uo,69 
68,253!,  10 
69,1631,50 


66,29  30,56  „,, 
67,2-.>'30,98l  ' 

68,1131,4° 
69*93'.  32'24 


82,81 
83,72 


84, 63  38, 57 
85,54(38,98 
86.4539,40 
87,36139,81 
88,271.40,23 
89,18540,64 
I  90,09,41,05 


7-;65  S3j49 
73,5633.9' 
74,47'34,33 

75«38  34-7i 
76,28,35,11 

77s'»9,35,55 

78,«o36,cc 

79,OI;36^ 
79,92*36,84 


3Zl33.  ||  8^73|37,6! 

37,74 

38,15 


^£PI_L^_ 

i  65 1  Deg. 


%4A^*-9 

86,fl7|a9»7: 

87,18  40, 1 1 

88,09^0,0- 
89,0041.0^ 

89,91 
90,81 

I  Dep.  Lat. 

[j>5^Deg 

•^—'•'••»:i.<»<yy 


74 

74 
76 

77 
78 

7.9 
80 

8t 

So 

83 
84 

85 
80 
87 


>9 
91 

9"  H 

93    \l 
94 
95 
96 

97 


lOO 

—     Its. 


Q  U 

cr^ 


TRAVERSE    TABLE. 


32 

25!  De?. 

*ti  Deg. 

=—  ^-?^D^ 

^  4«             ^S            ^\     #*  j 

,a  .    D'-p. 

Lar. 

Dep. 

[.,\\~ 

Dep. 

Lat. 

Dep 

=5     ^ 

i 

0,91 

0,42 

0.9'' 

o,43 

0.9' 

o  43 

0,90 

0,44 

l 

2 

i.8j 

0,85 

u8: 

0,85 

1,51 

o!86 

1,80 

0.87 

2 

g 

2.72 

1.27 

2  7 

1,28 

2,71 

1.29 

2,7° 

1  }3° 

3 

4 

3,6- 

169 

3-,6/ 

1,71 

3^6' 

1,72 

3:  60 

i»74 

4 

r 

4,53 

i,ir 

4*52 

2,13 

4-51 

2,15 

4,5° 

2,17 

5 

6 

5,4-] 

2  54 

5,4-' 

2-56 

5.42 

2,58 

5  5  4° 

a,6i 

6 

7 

6  34 

2,96 

6-33 

2,99 

6,32 

3,°i 

6,30 

3.04 

7 

8 

7,2.5 

3,38 

3-41 

7,22 

3>44 

7.21 

3,48 

8 

o 

8  16 

3.80 

S'M 

3  84 

8,12 

8,11 

9 

i  •> 

9,"f 

4.23 

9,04 

4.27 

Q-03 

4,31 

9,01 

4,34 

10 

1  ! 

9?  97 

4^5 

9  95 

4,69 

9-93 

4^74 

9,()i 

4,78 

1  1 

.12 

-,S, 

10,85 

1J!^0 

io58i 

5,21 

12 

13 

'•7'" 

5  49 

11,7* 

5,5,5 

1  1,73 

5.6o 

11,71 

5,65 

13 

14 

2,63 

12,66 

5  97 

12,64 

6.oq 

12,61 

6,08 

14 

1  l 

3  5«> 

6,94 

13,57 

6,40 

13,54 

6',46 

13,51 

6,52 

15 

1  6 

4  ?5° 

6,76 

14,4; 

6,83 

14,44 

6,89 

14,41 

6595 

16 

17 

5*4' 

7,18 

15,38 

7»2;5 

!5.3i 

7,32 

15,31 

7,99 

17 

i:' 

6  .  3  . 

7.61 

1  6.2o 

7,68 

16,25 

7-75 

l6:21 

7,82 

18 

i  .. 

7j-t5 

803 

17.18 

8  jo 

17,13 

8,18 

17,11 

8,25 

'9 

?_., 

3  ig 

l^ot; 

8  53 

1  8,05 

8,61 

18,01 

8,69 

20 

rt  1 

1U<7 

18,90 

8.96 

18,95 

9  °4 

18,91 

9?12 

21 

29 

9.94 

93^ 

19,90 

9-3^ 

19,86 

9,47 

19,8, 

9.56 

22 

23 

2'>,8 

9,81 

19,76 

2^,72 

9»99 

23 

24 

->r,75 

10,14 

21,73 

10,24 

21,66 

10,30 

21,62 

I'M  3 

24 

&5 

22  66 

22,61 

I0;66 

22,56 

10.76 

22,52 

10,86 

25 

?6 

-3'5('' 

i°5.99 

Z3j,59 

11,09 

23.47 

u,io 

23.42 

11.30 

26 

0     , 

^4  47 

11,41 

244* 

11.52 

24,37 

11,62 

24*32 

n,  7? 

27 

28 

-  VV 

^5.3 

11.94 

25,27 

12,05 

25-  2  £ 

12,  If 

28 

29 

25:28 

12,26 

26,2? 

26,17 

12.48 

26,12 

12,6o 

2  9 

22 

27.i9 

I7.,6k 

27..!' 

i258o 

27,08 

15,92 

27,02 

13,03 

Ji? 

3' 

18.1 

iy,iii 

28,04 

13,22 

27.9^ 

»3'35 

87,98 

i3>47 

3i 

32 

29,00 

13.5^ 

28,04 

13,65 

28,88 

13!  78 

•28,82 

139^ 

32 

8u 

29,91 

13,95 

29,85 

14,08 

29:79 

14,21 

29,72 

14.34 

33 

34 

;o  8- 

M-37 

3;J»7,f/ 

14,50 

30,69 

14,64 

30,62 

i4>77 

34 

35 

31,7* 

M>79 

31,66 

14,93 

3T>59 

»5>°7 

31-5? 

15'*1 

3£ 

36 

;<2,ijp 

15.  «r 

32.56 

15,36 

32.49 

15.50 

32,43 

15,64 

36 

37 

3.)  -5.'.' 

'.I  64 

33,4<> 

33-4C 

15.93 

33-33 

16,07 

3l 

38 

3  4  »4  4 

(6,06 

34.37 

16,  et 

34,30 

34>2c 

16,51 

38 

39 

-55  -35 

16.48 

35-27 

16,64 

35.2« 

16,79 

35,13 

16,9. 

39 

4_ 

16.90 

36jt£ 

17.06 

36-10 

17   22 

86*03 

17,38 

12. 

41 

*7»i6 

*7,33 

37,oi< 

17.49 

37,01 

15,65 

36,9; 

i/»8' 

41 

42 

38,06 

•7,75 

37,9' 

I  7-Q2 

37,91 

18,08 

37,8° 

18,25 

42 

43 

38,97 

18,34 

38.81 

18  51 

38>73 

18,68 

43 

44 

:9,88 

'o'6o 

39^8c 

18,77 

39,7' 

^,94 

39^3 

19,12 

44 

4  /? 

^0,7^ 

I9,OB 

4'>,7 

<9.20 

40,6; 

4°j5: 

19:55 

45 

47 

42;  & 

19  44 
.9,86 

41,6 

42,51 

19.62 

20,05 

42^42 

i9'58o 
20,23 

42,3 

19,98 

20,42 

46 
47 

4K 

13;  5'. 

20.29 

43,4* 

;o,48 

43»32 

20,66 

43,2 

20,85 

48 

49 

44,41 

20,71 

44.32 

20,90 

44*23 

21,10 

44,1 

2i,ac, 

49 

,f. 

i5«3* 

-1,13 

45»  2'- 

21,33 

45,1  g 

21  j53 

4?,O< 

21,72 

£1. 

5?- 

r"£ 

ff8- 

Lar. 

Dep. 
64  1 

Lar. 
Deg. 

T)ep 
64^ 

Lai.' 
Deg. 

i->ep  Lau 
64*.  Deg. 

* 

TRAVERSE     T  A  B  L  E. 


§1 


GT 
5,46,22 


48,03 

48,94 
4.9,85 

50,75 


5- 


,54 


57 


51,6624 


60 

6. 
62 
6? 
64 
65 
66 
6 


53 

•& 


22,40 

22, 


52,57 
.5953,4 


21^8 


24.51 


54,38*5.- 
55,2825,78 
56,19  26,20 
?7,I026,62 

!,oo 
58,9ih7,47 


tSJ7\/7St 

5958227,89 
_     60,72^8,32 

6861, 63128,74 
69,62, 54^29, 16 

7J63,44'29,5g 

7li64«35J3°,01 
72,65,2530,43 
7366,1630,85 

74i67,073i,27 
7567,973!, 7° 
7668.8832,11 

77|69, 79:32, 54 
7870.6932,96 
7971,6033,39 
8j2£i£? ;  ° 

8i|73,4i34,23 
8274,3234,65 
8375,2235,08 
8476,1335,50 
85(77, 0435,92 

86i77,943635 
87)78,85 
8879-7637 
RnHto.66  o*';6i 


91182,4738,46 
9283,3838,88 
93  84,2^  39,30 
9485,'939573 
95  86,4 «  40,15 
9687,01 
9787,91  40,99 
9888,82  41,82 
9989,72  41,84 
,  iof>9o,63 
_  iJ7D>i_  ^ 

fa  65  T5^ 


De       0 


_57  38_/H      8 1,40  3_^_,^Q 


IP 


««£HM 


T    R  A  V  E  R  S  E    TABLE. 


«3:s 

^  p. 

26  Deg. 

261  Dee. 

26  \  Deg. 

2  6  \  l)eg.     ^j  p 

W  5= 

Lar.    Dep. 

La.'.    Dep 

L*  . 

Dep. 

Lat.    Dep 

_&_' 

i 

0,90 

0,44 

0.90 

0,44 

0,89 

o,45 

0,89 

0-45 

i 

2 

1,80  0,88 

i*79 

0,08 

1,79 

0,89 

1,79 

0.90 

2 

3 

2,70   1,32 

2,69 

'*33 

2,68 

1,34 

2,68 

x,35 

3 

4 

3.6o    1,75 

3,59 

1,77 

3,58 

1,78 

3-57 

1,80 

4 

5 

4:49    2,19 

4.48 

2,21 

4,47 

2,23 

4,46 

a,  25 

5 

6 

.5-39;  2,63 

5,3* 

2,65 

5,37 

2,68 

5,36 

2,70 

6 

7 

^---X!    3;°7 

6,28 

3,*<> 

6,26 

3,12 

6,25 

8 

7>*9   3,51 

7,i7 

3,54 

7,16 

3<57 

7,14 

sle5 

9 

8»°9    3,9,5 

8,07 

3,98 

8,05 

4,02 

8,o4 

4,05 

9 

J 

10 

8  99|  4*38 

8,97 

4,42 

8.95 

4,46 

_8,93 

4.50 

10 

1  1 

9,  by   4.82 

9*87 

4  87 

9.84 

4.91 

9,82 

495 

1  1 

12 

10,79 

5,26 

10,76 

5.31 

10,74 

5^35 

10.72 

5,4° 

12 

1  3 

11,68 

11,66 

5,75 

ii,  0*3 

5.80 

^,61 

5,85 

13 

A  <j 

12,58 

6^14 

Ia,56 

6,19 

12,53 

6.25 

I2,50 

6,3° 

H 

15 

13,48 

6,58 

13,45 

6,63 

13»4a 

6,69 

^,39 

6,75 

'! 

16 

14,38 

7>or 

14,35 

7.08 

14.32 

7.14 

14,29 

7,eo 

16 

1  7 

15,28 

7,45 

15,25 

7,52 

15,21 

7*59 

J5'i8 

7,6,- 

J7 

•*  / 

1-8 

.6.18 

7,89 

1.6,.  14 

7,96 

16,11 

8,03 

J6,o7 

8.10 

18 

1Q 

17,08 

17,04 

8.40 

17,00    8,48 

J6«97 

8,55 

J9 

•*  :? 
20 

17.98 

8,72 

*7*9_4 

8,85 

17.  4^    8.92 

^.^j^jOo 

20 

21 

18,87 

9,21 

18.83 

9,29 

i8,79    9-37 

18,75 

9»4.r> 

21 

22 

*9,77 

9,64 

19,73 

9  73 

19,69    9,82 

'9,65 

9-90 

22 

23 

20,67 

10,08 

20,63 

10,17 

20,58  1.0,26 

" 

23 

24 

21,57 

10,52 

21,52 

1  0,6  1 

2i.48io,7i 

21^43  i'-,8o 

24 

25 

22,47 

1,0,96 

22,42 

1  1,06 

22.3711,15 

22,32 

!I,25 

25 

26 

23-37 

11,40 

23,32 

11,50 

23,2711,60 

23.22 

11,70 

26 

27 

24*27 

11,84 

24,22 

11,94 

24,1612,05 

24,  1  1 

12,15 

27 

28 

25,1112.38 

25,06  12,49 

25^00 

12.60 

28 

20 

26,'  6|  12,  71 

26,01 

12,83 

25,9512,94 

25  90 

13.05 

29 

J 

3° 

2^19613,15 

26,91 

13,27 

26,85  13-39 

26,79 

13,50 

_3£ 

31 

32 

27-,86  13,  59 

27,80 

28,70 

il''5 

28*6414.28 

27,68 
28,58 

13»95 

3* 

O  " 

33 

29,6614,47 

29,60 

14,60 

29*53  14-72 

*9,47 

14-85 

.33 

34 

30,56  14,9^ 

3°'49 

15,04 

30,^3  15,1  7 

3  '*36 

15,3° 

34 

35 

31*4615,34 

3**39 

»5*48 

3I>32;15»62 

31.25 

15*75 

35 

36 
37 

32,3615,78 
33,26116-22 

32,29 

15,92 
16,36 

32,22116,06 
33-  11  16,51 

33*04 

16,20 
16,65 

36 

37 

38 
39 
40 

34,1516,66 
35-05iI7»i° 
35,95jt7.53 

34^08 
34,98 
35*87 

16,81 

17*25 
17,69 

34,01 

34,9° 
35,8o 

16,90 

17.40 

33,93 
34,83 
35,73 

17.10 

!7>55 
18,00 

38 
39 
-JL2 

41 

3^,85  17.9? 

36,77 

18.13 

30.69 

18,29 

36,61 

18,45 

41 

TT 
42 

37*75l8>41 

37.67 

18,58 

37*59 

18,74 

37.51 

18,90 

42 

43 

38.65(18,85 

38,57 

19,02 

38,  48 

19,  19 

38*4C 

i9,35 

43 

44 

00.55 

19,29 

39>46 

19,46 

39,38 

19,63 

39,29 

19,80 

44 

45 

4°  ,  45 

1-9,73 

4^,36 

19.90 

40,27 

20,08 

40,18 

20,25 

45 

46 

20,  1  7 

41,26 

20,3-5 

4i,i7 

20,53 

41,08 

20,7 

46 

47 

42,24 

20,60 

42,15 

20,79 

42,06 

20,97 

4J*97 

21,15 

47 

48 

*X     ,  -^^r 

21   04 

43,05 

21,23 

42,96 

21,42 

42,86 

2  I  .  60 

48 

49 

44,0421,48 

43,95 

=41.67 

43,85 

21.86 

43,76 

^2,05 

49 

~ 
i    cS 

44,9421^ 
DepJLat. 

44,84 
"De"p. 

22,11 

44.75 

S™ 

44,65 
Dep. 

[Jr. 

.Jl0. 

¥    * 

J  Q      64    Deg.    1 

63}    Deg. 

63!  Oeg. 

63^    l^g' 

a  8 

T  R  A  V  E  R  S  E  T  A  B  L  E. 


65 
66 
67 
68 
6.9 
Zil 
71 
72 

73 
74 
75 
76 

77 
?8 
79 
8_1 

81 
82 
89 

84 
85 
86 
87 
88 
89 
9_L 
9! 
92 
93 
94 
95 
96 
97 


1  Q 


.56,62 
57,52 
58,42 
59, 3  * 
60,22 
61,12 
62,02 
62^92 

63,81 
64,71 
,,6. 
66.-5> 
>7,4! 
68,31 
6.9,21 
70,11 
71,00 
71,90 


72,8^ 
73,70 
74,60 

75,5° 
76,40 

77,3° 
78,20 

79,09 

79,99 
80,89 


27,62 
28,06 


28,93 
29-37 
29,81 

30,69 

3J,56 
32,oo 

32,44 
32,88 
33,32 
33,75 
34,J9 
34,63 
35,  "7 


35,95 
36^88 


37,7" 


38,14 
38,58 
39,oi 

a9>4? 

8 ',79  39,89 
82,69 


7 '42 
7,86 
57,402^,31 
3028,75 
29,19 


<? 
59, '9 


63,68 

6?,47 
66,3/ 
67,27 

68,16 
69,06 
69,96 


72,65 

73,54 
74-44 
75,34 
76,23 

77,13 
78,03 

78,92 


79,82 


60,0929,63 
6  -,9930,08 


30.06 

31, '84 

32,29 
32.73 


34'5° 
34,94 

35.38 

35,83 
46  27 
36,71 


37,59 
38;oi 

38,48 


39,36 


56,38 
57,28 
58,17 
59, °7 


28,11 
28,56 
29,00 

29>45 
29  90 


59,96    _  . 
6o,86  30,34 

30,79 
62,6531.03 

63,54 
64,44 
65,33J3e,57 

67,1233,46 


68,91 
69,80 

70,70 


72,4(, 

73:38 

74,28 

75,1737,48 

76,0737,93 


76,9(1 

77,86 
78,75 


79,65 


34  36 
34,8o 
35^5 

s^rj 

36,5) 


38,37 
38,82 

39.27 


39,  7 


26! 


U<:p 


45,54 
46,4323,4^  52 

47,3;r"°":l 
48,22 

49,11 
50,01 

5^,9° 

51,7926,11 

53,59*6,56 


24'd  54 
M,76  55 


25,66 


55,36:27,91  62 
56,26  28,36;  63 
57,i5's8,8i|  64 
58,04129,26  65 
58,94'29,7i  66 

60,72  3o,6i|  68 
6 1,62' 3 1, 06  69 


65,1.9  3 *>86 
66,o833,3i    7 
66,9733^61  7 
67,8734^  ' 


/i 

72 

"3 
74 

"5 
76 

wu,  -o  34,^^1  77 
69,6535,11!  78 
7^,55  35,56  79 
7M4  36^01  80 
72,3336,46  81 
7 3,2 2  36,9 1  82 
74,1237,36  83 

75»9o:38,'26 


«y 

86 

//5v/y  o/,-  Jj    87 

78,58  ^9-6i   88 
79.4o4°,o6   89 

O.-^    ^^^'jri    e  i      O1) 


56 


T  R  A  V  E  R  S  E     TAB!,  E. 


2  74   Deg. 

Lat 

Dep 

0.9 

2$ 

it] 

3»5 

1,86 

4,4 

2,33 

5,3 

2,79 

6,1 

3.26 

7,o 

3,72 

7,9 

4>i9 

8,8 

4,66 

9,7 

5,12 

10,6 

5,59 

11,5 

6,05 

12.3 

6,59 

13.2 

6,98 

14,1 

7,45 

15,04 

7.9* 

15,9 

8,38 

16,8 

8,85 

17,70 

9,3i 

18,58 

9.78 

19,47 

10,24 

2J>35 

10,71 

21,2, 

11.17 

22,  12 

11,64 

as'**! 

12,57 

24,78 

i3?97 

27  43 
28,3, 

4-43 
4,90 

29,20 

5'37 

3°»09 

,5,83 

30,97 

6,3" 

31.86 

6,76 

32,74 

7,23 

33.63 

34,.5i 

8.'62 

36,88 

9>0c> 

37,17 

9,56 

38,05 

0,02 

38,94 

0,49 

40,71 

1,42 

41,59 

.88 

42,43c 

.2,  -5  c 

13.362 

2,8. 

44,  ?.  .5  2 

3,28 

i>ep.  J 

^a-. 

62}  Deg. 

8 

4s 


TRAVERSE    TABLE, 

**=— E=S 

n   P|   27    l*g. 
5?    ~!La  .    Ueu 


57 


5V45  4^ 

53J47,2* 

'  "        24,52 
24,97 
56(49,9('  25,42 


59152,5  7120,7V 
60153,4627,24 


6255,24 


64i57»<>*  29,06 


46,23^3,81 
47,12:24,27 
48,01124.73 
48.902.5,18 
49,7825,64 
,5  56726  10 
51,5626,56 
.52.4527.01 


54^3*7,93 


56,01:28,85 
56.901  Z9.  30 


l)e?. 


L'i- 

47,24 

46,12 


•,:5,  IH^'S 

-2 .}..    i    il  46,C2 


47,01124,47    jj   4P.90 

47,9 -N  93  |j  -i7»7i 
48,79    5  40  i*  40.0} 


45,67  25,86 

5o,56Je6, 
51,  4.5126, 


1. 

M'99'28,63 


5°?44 

52,21 
53  io 
53-98 


55,75 


66|58,8i;29,96 

67'59 ••  7°  3°  42 
68^0,59:30,87 

£961,4831,33  .,  r_iW  ,„.  , 
7_;62.B9  3M8  0^03  3^05  | 
7,63,2632.23  I  63,ia,£  - 

_!.£...      -w.Irtrt     Ar\     if     r\A.i)\\f. 


0,90:4^.30      50,77199.55   1 

7, "9^29,76      67566l3!!>01  I!  •^7''5& 

8,68o>)  22  I   58. 54  3-- .48  |>  5--41 


5y-43!3  S94i|5?»2c 
6  >32:3^  6i 

6 g.oo'.:;  2  3 ^  |j  ^.i9A 


26,07 


26  4 

28,87 

^33 

z9 
3  - 
30-78 


2.1 


74'165.93:.-3,6  ' 
75,66,83  34  -5 
76,67,72,34,50 


64,01132,9?  !]  63,85:33,25  ? 

6-i»75^3  =  7i  i\ 
6^79'33,8i  jj  6i'64;34;' 
66,68(34,34  ||  66,53-3^63 

67-57|3458° 
68,45ks»fi6 

69,34135,71 


797°-3935--7 
8   7i.>o3o  :-u 

i  8T72-£73(:.7; 
82:73^c6'37-28 
83J73"95;37  6B 

8V75-74!38.59 
8676,!'3:39-  4 
8777,52  39:5 
88-78,51 
8979-3' 


67^41!35-°9 
68,3'  :i'^5 . 5  c  I 
69.1936,02  |f 
70,0716  4^  |i  5'^9I 


40.41 


Q'  J8o.  19140,86 


91!' 

9'4 
9382,8642,22 


t2,68 

43, J  3 
13,58 

14,40 

't5-4° 


Q    63   Dtg. 


94    „ 

84,6.5 

9r>  85,54 
9786,4; 

^32 


7^,9 

7^68 

75,57 
76,46)31 

77,3.4 

4  --.29 
4«  75 
it. ai 


38.00 
38,46 
38  92 


/    '  *      *  ^     •    /  •  -j-  -     t  * 

72,78:37  S6  ||  7--51 
73:62|3-;33  U  7:^" 


74,5! 

75,4" 


o 

8o,y 

8216^ 
83,57 


85-35 

86,23 

87,12 

880 
88,9 

Dep 


'l^;/^    If    74>< 

39  »i)     "- 

39.71    !      76,1 


^2, 


42,58 


H-41 
I4.»7 


78»«;64^i63 

78.94141,10 

£9^834-1^56 

8-J.72  42,02 

:J2     48 

83,49   i2. 
83»38 


85,15 

86  ^4 
86-93 


L) 


H,4  > 
43,87 
44-33 


45:7  » 


Deg. 


62 

63 
64 
65 
66 
67 
68 
69 


71 
72 

73 

74 

7*6 

77 

78 

9 


57-^5 

57-71 

t^6j 

;.9  5 
40,0^ 

to  5 . 
io  9' 

M»44 

i  i   q 


8i,4 

43-3( 

84,° 
84,9 
85  8  , 

87^61  46!1 
8>J,5_  U6\y( 

D   "'La^. 


39 
90 

77    ii 


93 
94 

96 
97 
98 

99 

lOO 


IS 

4^"^  ^'3 
-4,-<      Hv 


$8 

&.G& 


TRAVERSE    TABLE. 


J 

2 

3 
4 
5 
6 

7 
8 

9 

10 

1 1 

12 
13 

15 

16 
18 

20 
21 
22 
23 
24 
25 
26 

28 

29 
30 


32 

33 

34 

% 
II 

3.9 
-4JL 
4i 
42 

43 
44 
45 
46 

47 
48 

49 

5o 


0,88 


Deg. 
Do  p. 

0.4.7 


Ji77 
2,6,5 

3:53 

4j4» 
5-3° 
6,18 
7,06 

7,95 


10,60 
iM8 
,2,36 
'3,24 


15,89 
16.78 
17,66 

18,54 


20,31 
21,19 
22.07 

23-84 
24,72 
25,61 
26.49 


0,94 

i,!88 
2,35 
2,82 

3*76 

4.23 


7.51 
7,98 


9j9. 
9,86 

io?,8o 

11,27 
^,74 

12,21 

12,68 

13,15 


14. 


28,25 
29,14 
30,02 

30.90 

32;'67J 


M,55 


15,49 

16-43 
[16,90 


34.43i8,3i 

35i3-3  111? 
36,2019,25 
37,08^9  72 
37-9-20,19 
38,85^,66 


40,62*2 1,60 


cp 


2,37 
2,84 

3,3i 
3>79 


7,93 
8,81 

9,69 
io>57 
n,4^ 
12,3: 


18,5° 


32,55 

33,4 

34,3 


42,2 


l>o.'Lat. 


i7,°4 

17:51 

'7,99 
18.46 


:0;83 


.3.67 

,at. 


2'L 
Lai 


SF^ 


1,76 
2,64 

4,S9 
5,27 
6,15 


7>9J 
"9^67 

11,42 
12.30 

14,06 
J4>94 

ii>6 

17,58 


20,21 

21:97, 

22,85! 

23>73 
24,61 

25»49 
26.36 

27,24 
28,12 


3° 


6 


3i,64 
3  3  -39 

3M7 
40,48 

43  94 
HlP: 


Deg. 

2.8J  Deg% 

^£P: 

Lat. 

3eo 

o,48 

0,88 

0.48 

°>95 

1,75 

0.96 

M3 

^563 

1.44 

*;9i 

3-51 

1,92 

2,39 

4,38 

2,40 

2386 

5,26 

2,^9 

3,34 

6,14 

3,37 

3,82 

7,°i 

3,85 

4,29 

7,  Be 

4,3? 

4.77 

8,77 

481  . 

5,25 

9,6^ 

5,29 

5-73 

Io'52 

5,77 

6.20 

11,40 

6,25 

6,68 

6,73 

7;   l6 

3jl  A 

7,21 

7j63 

14,0? 

7,70 

8,n 

I4,9r 

8.18 

8,59 

15.78 

8,66 

9>°7 

X6.66 

9,14 

Q'54 

J7-.53 

Q.6<; 

10.02 

l8;4l 

10,  1O 

10,50 

19^,29 

1  ',58 

10,97 

20,16 

1  1,  06 

1  1,45 

2l   O^ 

i;  ,5^ 

IJ;93 

21  '92 

12,<  2 

12,41 

22,79 

12.51 

12,88 

23.67 

12,99 

13,36 

I3t47 

13*84 

»5,43 

13,95 

14.31 

26,30 

'4,43. 

,14.79 

27,1^ 

14  9i 

28,0^ 

r5r39 

>  15*75 

28,9: 

15,87 

>  16,22 

29,81 

16  35 

)  16,70 

30,69 

'M3 

H7.18 

S»«5< 

17.32 

M8^3 

83,3' 

1^28 

18,6  1 

'8,76 

J  '9^9 

3.5><>f 

19,24 

3  19,56 

35,  9^ 

19  72 

1  2v,04 

36,8 

J-,2C 

)  20.52 

3?.  7^ 

20,68 

7  20,99 

38,5 

ai,i6 

"  *M7 

39,4, 

11-64 

]  21.  95 

4",3 

^2,13 

:  *2>43 

41,2 

^2,61 

^  22,90 

42,08 

23,  C'9 

'  23,38 

42,96 

23,57 

123,86 

43,84 

23.  i>5 

.Lai. 

La 

;  Lteg- 

6  i-l-   beg 

£5$ 


9 
10 

1 1 

12 
13 
14 
15 
16 

17 
18 

19 
2O 

21 

22 
23 
24 
25 
26 

28 
29 

_3o 

32 
33 
34 
35 
36 
37 
38 
39 
42 
4i 
42 

43 
44 

45 
46 

47 
48 

49 
*o 


**a^ 


TRAVERSE    TABLE. 


28   Deg. 


at. 


Jep. 


5.03 

ni 
6,80 

7,68 

9,45 
o.33 

2,09 

M8 


3,8f 
4»7' 
5,6, 

6,51 
7,3S 


2,6 
3,5 
4,4< 
5,3 
6,2 


8,8 

9>£ 
•70,6 


2,4 

73,2 

74,1 
5,° 
5,9 

76,8 

77,7 
78,5 
79.4 

8  ,3> 

81, 

82,11 

83,' 


3>94 
4,4* 
4,88 

5,35 
5,82 
6.29 
6,76 

7,7° 
:8,I7 


284-    Deg. 
Lat. 

44,93 


8,64 
'.9l58 


A5 

3«i39 

32,86 


33,33 


34,74 


35,68 

36,15 
36,62 

37,°9 
37,56 

38,03 

0^,97 
39,44 


40.37 
40,84 

41,78 
42.2,5 


87,41 


42,72 


43>66 


85,65  45,54 
86,5346.0 


46,48 


88,2946,95 
Dep. 


l  at. 


*&Sft 


62  Deg. 


46,69 

7,5? 
43,45 
49,33 
50,21 


52,8 


53,73 
54,62 

55,50 
56,38 
57,26 
58,14 


59,9 
60,7 


62,5 
63,4 


65,  ifi 

66,0 

66,9, 

67,8 

68,7 

69,5 


72,2 
73,1 

73,9 
74.8 

75,7 
76,6 

77,5 
78,4 

79£ 
80,1 
81,0 
81,9 
82,8 


87,2 
88,0 


6  if 


4,61 

5>°9 


6,o3U48,3< 


44,82 
45,7o 
46,58 


7,45 


50,09 

50,97 
5',8< 


8,87 
9,35 

0,29 
o,77 
1,24 

2,19 

2,66 
3«J3 


3»6i 
4,08 

4>55 

5:°3 

5,50 

5,97 
|645 
}6,9* 
57>39 


38,81 
39,29 

39,76 


4^65 
42,13 
42,60 


43»°7 
43,55 
44,°* 
14,49 
14,97 
15,44 

46',39 

17,33 

Lat. 


53,6i 
54,49 

155,37 
56,2 
57,12 
58.00 
58,8» 

[59,76 
60,64 
£ll5J 
62, 4( 
63,27 

65,0; 
65,9 
66,7- 
67,6 
68,5, 
69,4 
70,3 


72,0 
7^9 
73,8 
74»7 
75,5 
76,4 
77,3 
78,2 

79,0 

79)9 
80,8 

8i,7 

83^4 
84,3 

86^1 
87,0 
87,8 


Dep 


5,77 

6*72 
7,20 
7,68 

V5 
8,63 

9,58 

,0,06 

°,54 
i, 02 


,45 


34,36 
34,83 
5,3i 
-5,79 
36,26 

36,74 

37>22 

37,70 
38,17 


38,65 

39>.'3 

40,08 
40,56 
41,04 


42,47 
42,94 


43,9C 
44?38 
44,85 
45,3c 

4^28 
46,7^ 
47>£4 
7-7^ 
Lat. 


Deg.    I!  6i|  Deg. 


Dep. 


45,59 


:8,22 

49,10 

49,97 
50,85 


25,49 
*5,97 
26,45 


17,9° 


52^60  28*^86 


29,34 


3o,3 


3i,z6 

*rt* 


I:S 

59,62133,71 
60,4933,19 


62,25*34,1 


64>88j35,5< 
65,7536.-07 
66,6336,56 

68*38,37,52 
69,2638,00 

7o.n'38,JL8 


59 

S5* 

sr 


51 

52 

53 
54 
55 
56 
57 
58 
59 

6-> 
61 

§ 

64 

65 
66 
67 
68 

69 
70 


71,01:38,96 
7i,89;39j44 


74 
75 
76 
77 
7« 

79 
80 

81 
82 

/•*•?'  /,'-'-"•'  O 

73,644°=!^  84 

74,5*;40,38|  _^ 
75,4°'4I,36  86 
76,28 4',85  87 
77,i5'42,33  88 
j%to^M  89 

79^78J43577  9^ 

8i,54'44,73  93 
82,4ii45,aij  94 
95 


84'17iV^ 
85,0446,66 

85,92,47  .-14 


96 

97 
9» 

,     ,„_-       99 
87,67148,  loi  oo 

Dep.(Lat. 
Deg 


6,1 


*  ^L 

,  5  a 

***&& 


6o 


TRAVERSE     TABLE. 


m 


?9|  M'J2> 

LatT 

^ep 

0,87 

o,'5'.i 

1,74 

0.99 

2,60 

l,49 

3»47 

1,98 

4,31 

2,48 

5,2i 

2,98 

6,08 

3-47 

6,95 

3,97 

7.81 

4»47 

8.68 

4»f)6 

9:55 

5»4^ 

10,42 

5'95 

i  ^*P 

6,45 

12jl/; 

6?95 

13»    2 

7-44 

1389 

7,94 

14,76 

15,6-5 

4s 

16,50 

9,43 

17-3^ 

9.92 

19,1' 

10,92 

19,97 

11.41 

20,84 

11,91 

ai»7> 

12,41 

22,57 

12,90 

^344 

(3,40 

24>3' 

3'  89 

25,  ib 

>4  3.9 

2^.0', 

1  4,81; 

26,9  i 

5-S 

27.7;- 

,5,88 

28,  6< 

(6.38 

29>5- 

16,87 

3°?3i/ 

1.747 

31.  2< 

t;j?6 

3  2  9(/ 

,8^86 

^86 

!9-35 

35,6° 

W~v~ 

36,46 

10& 

38^ 

2l)8j 

3.95o? 

22,33 

39-94 

22.83 

40.81 

J3  3^ 

41.6? 

J3,8'2 

42,5i 

i4-3I 

43  41 

'4.81 

Dtp. 

I^a-. 

6ol  Deg. 

Q 


TR 


E  TABLE. 


igj.nee. 

29|  Dee 

U. 

D    x> 

Lar.    Jjrp. 

44»3< 

)   5  il 

4,2 

25,3: 

45,  2( 

45-1 

^580 

45.  ic. 

^|IO 

45,,- 

i6,'^c 

47,0,° 

26.59 

46,8 

26,8', 

47,8- 

'  7  ,  -  ;  iS 

^7,75 

27,29 

48.74 

27.5S 

48.6 

-7.79 

49,6i'e8.o7 

49,4( 

i-S  2;-, 

50.48 

28.56 

50,3 

8,78 

5«,35 

29,0? 

52"'* 

29.28 

'  |  •  x  v  ' 

52,9 

3  -27 

53-963^53 

53-8 

•^•7? 

54,83  3i»02 

54.-7 

31,26 

5,5,  *c  31.52 

55,4 

•>  ?»7 

56,57|32,oi 

56,4 

32,25 

5754^*13  ^}<5  ^ 

57,3 

i  -  ^  / 

58,3132,99 

5«,i 

]3,2.; 

59,  '8 

33,48 

59,<M 

J3  7-; 

6-,o5 

^3,98 

5^>9 

,J4--'i 

34,47 

60.77 

34-  ^ 

61,8 

34.96 

6t,6_ 

35,  a3 

61.67 

35;  45 

6a,5 

35,73 

^54 
64,41 

35j95 
36,44 

64,25 

3^7- 

6^,28 

6$,ii 

37,*2 

66,15 

37-42 

65-9 

37,  7  i 

$7,02 

3792 

66,85 

,8.2' 

67.89 

'67,72 

^.O*  "  C 

68,76 

18,9  - 

68,59 

39,  2< 

S.  6; 

39  39 

6.)   4 

•<9-7 

70,5P 

39,89 

7o,3' 

to,  19 

7',  37 

7«-Jc 

^0,69 

72,24 

4^7 

72,0(5 

i  i  ,  i  '-' 

'3,11 

4  ',36 

72,93 

ti,68 

73,98 

11.86 

735**? 

2jlo 

74,8/' 

is  25 

74,67 

1  2  fc; 

75,7£ 

42,84 

75,53 

43.17 

76,5( 

43,33 

"6,40 

t  i>6; 

77,46 
'83^ 

43,83 

44  -^ 

78.14 

14-  16 

4.66 

^9,2' 

14'8i 

79,01 

5,16 

$0,07 

79,87 

5565 

$0.94 

4  A  80 

80,74 

6.15 

MI 

16,29 

6,64 

?2,68 

46,78 

82,48 

7*14 

{3.55 

17,27 

83,35 

7,64 

!4>4« 

^5,29 

17,77 
48,26 

84,22 
85,08 

8.'6j 

{6.17 

48,75     85  95 

9-  '7 

57,0-1 
J  -,.. 

10.21  ?!  86,82 

—  F/  n  — 

PI    .  *  /• 

2:2! 

6oiDes.  1!    6o»-tteK. 

p.  a 


65 
66 

67 

08 

69 

71 
72 

73 
74 
75 
76 

77 

78 

79 
8_> 

81 
82 
83 
84 
85 
86 

87 
38 

89 


7  99 


"'  O 


T    R  AVERSE    T  A  B  L  .E. 


Q  u 

30  Deg.     *  --,1.  D,-T. 

eg 

£  P 

Laf. 

Dep.  j 

J  -        i  Uep. 

s   Lat.       e. 

:  " 

0,87 

0.50 

,o.80|  i.»,so 

0,51 

'o,B6 

""    ~7~ 

1 

2 

i,72 

1,00,, 

1,01 

J,  ")2 

1,72 

1,0  2 

s> 

3 

2,6, 

1,50 

2.59 

»55«   j    2,5b 

I,5a 

2.58 

1,53 

3 

4 

3,46 

2,00 

3,46 

2,02       3,45 

2  -  '-'3 

3-44 

2,05 

4 

5 

4,33 

4,32 

a>52  j    4,3* 

2,54 

4,00 

2-56 

5 

6 

5,9.0 

3,  op 

5  1  1  ^ 

3,02        5,1? 

3.  Qr 

5,16 

3,^7 

6 

7 

6^06 

35° 

6,05 

3»53  »    6>°3 

3^55 

6,02 

3,58 

7 

8 

6,93 

4,00 

691 

4r>°3 

6,89 

4,06 

6,88 

4,  n9 

8 

9 

7,79 

4^5° 

7,7? 

4-53 

7»7.r 

4'57 

7,73 

4  60 

9 

10 

8.66 

5,00 

8,64 

5  04 

8.62 

5,11 

10 

1  1 

9,53 

5.  ,50 

9*5° 

5,54 

94% 

~5^ 

~^4-5 

"pa 

1  1 

12 

to»39 

6,00 

I':>?37 

6-05 

10?34 

^.09 

I°«31 

6.  14 

12 

13 

ll;,«6 

(\    r,o 

M>®3 

6,55 

jri,2t 

6,60 

?i,i7 

6,65 

'3 

14 

U,12 

7,00 

1  2,09 

7,05 

12,06 

7.11 

r2.oS 

7.16 

14 

15 

12,99 

12,96 

7,56 

12.92 

7,  6  1 

I2.8'/ 

'7,67 

'5 

16 

13,86 

8,00 

13,82 

8,06 

13,79 

8  ix 

1  9  '  <7  S 

8.18 

16 

17 

14,72 

8,50 

14,69 

8,56 

Ms 

14,6I 

8,69 

17 

18 

'5,39 

9,00 

15,55 

9,07 

15*51 

Q,  14 

1  ^.47 

9,20 

18 

19 

16.45 

10,41 

9-47 

16,37 

9^64 

J6.38 

9,71 

19 

20 

L7>3? 

1  0,00 

17,28 

I7,^3 

IO.T5 

10,2,^ 

20 

21 

18^9 

lojTo 

18,14 

lo^g 

18,09 

Jl.  OjClfa 

1.8,05 

£•',74 

~2~! 

22 

19,05 

11,00 

19,00 

1^,08 

18,90 

11,17 

18;91 

11.25 

22 

03 

^9:92 

11.50 

19,87 

11.59 

19,82 

II,<57 

19,7' 

11,76 

2Q 

24 

80^78  12,OO 

90,73 

'•  2  .09 

eo,68 

12,l8 

»o,6s 

12,27 

24 

21,65 

12,50 

21,60 

i  p.-  5  9 

21,54 

12,69 

ai>49< 

12.78 

2  5 

26 

225<52 

13.00 

22.46 

13,10 

22,40 

13,20 

22,34 

[3>29 

26 

2^ 

23.38 

13-5° 

i  t3,3-> 

13.60 

23.26 

13.70 

23^ 

13,80 

~7 

28 

84>25  I4)bp 

24,]9 

J4,n 

-4,13 

J4.21 

24,06 

14}32 

28 

29 

25i  i  1:14,50 

25,05 

14,61 

24,99 

14.72 

24,92 

14,83 

29 

3° 

;  -,.o<> 

25j9? 

'5511 

25,85 

15»23 

Zr}   7p 

15.34 

_3° 

3i 

!-fo*0 

261,7  & 

15,62 

•26,71 

!5>73 

26,64 

15»S5 

3i 

32 

".7.  7  1  iU'00 

27,64 

1  6    1  2 

27,57 

16,04 

*7,5° 

16,36 

32 

33 

28,58  16,50 

28,51 

16.62 

•28,4; 

16,75 

28,36 

16,87 

33 

34 

•  7.00 

29,37 

I7i*3 

29,3'> 

17.26 

29.22 

17-38 

34 

35 

go  H<j  1  17,^0 

30,23 

17,63 

3°,i6 

17,76 

3  v  c 

17.90 

35 

36 

3j,i8li8  <>o 

31.10 

18.14 

3ljoa 

18.27 

30,0^3 

36 

37 

32,04!  18,50 

18,64 

31.8; 

18,78 

31.  & 

18,92 

37 

38 

32.91;  19,00 

4«lf3 

19,14 

3^,74 

(9.  -29 

32,66 

19,43 

3B 

39 

33,  77J19  50 

33,69 

i9>65 

33-  6c 

J9//9 

33-52 

i  Q<94 

39 

_4° 

•'     'L'jfJ 

M4  -  .55 

20,15 

_4.*^  " 

2  *.  7O   i 

i   »4  A 

40 

4> 

}£,/;>  ii*--j5o 

35»42 

20,65 

35,33 

2  ;  ;  .  0'  I 

30,96 

4i 

42 

o6.37|ai.-o 

36,28 

21,16 

3<>,  ID 

11.32 

42 

44 

37,24'ii^o 

375i4 

•i  66 

2j.b»2 

3.0,6-5 

21.99 

43 

44 

q  -5.1  i!22,f'0 

38,01 

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4,10 


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49,19 
0,03 

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55,12 

55,97 


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7,°3 
27,56 
28,09 
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29.i5 
29,68 


1,80 


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32,85 


2833 


36,82 


8.5^ 

9,3° 

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61,9  i 


66,  i 
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6-.  84 


09,54 

70 


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71,24 


3,78 
74,63 

75,48 


70,0 

78,87 

79,72 

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34,44 
34,97 


16,56 

37,6s 
38^68 


39j74 
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42J59 

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3,45 
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15,57 
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48,75 
49,28 
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83,06:52.46  I 


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82,o, 
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44,822  ,28 
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47,3629,^8 
30,42 


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52.44 
53,28 

54?i3 
54,97 
55,8s 
56,66 


6. ',05 
60,89 
61,74 
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63>43 
64,28 
65,12 

65,97 
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31,48 
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4:68 

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35,75 
36  29 
36,82 
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39,49 


814 


41,09 
41,62 
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43.76 

44,29 
44,82 

45,589 
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46,96 
47,49 
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49- °9 
49,63 
50,16 

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52,83 


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44,70 

45,54 

46,39 

47 

48.07 

48,99 


2,3. 30 


5(,45 
53,Io 


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55,66 
56,51 

58,19 


59,8838. 


60.72 

6i>57 
62,41 


64,10 
64,94 


27,94 
48.48 
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30,63 


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33^5 
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34,9  B 
35?46 
36,00 

36,54 
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38,69 
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63,2540,30 


40,83 

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66,63 

67-47 

68,31 
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73',38 
74,22 
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42,45 


43-5^ 
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45,67 
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6.75 


77,5949,a3 
78.4449,97 


79,88 

80, 

80,97 

82,65 
83,5 


48,89 


50,51 


5 ',58 

52.  12 
52,66 

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3.6     «4-3-i  53,73 
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46,26 


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94,3° 


28,13 


29,11 
29,75 
30,29 
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33,°° 
33,54 


53»83  34,6s 
54,6735,16 
55-5J!35,7o 


58,c3;37533 
58.8737^7 


62.2440,03 


63,7641,65 

65,61,42,20 

66,4442; 


68.07J44-36 

71,49:45,9^ 
72,3346 

73, '747 

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75,694^69 

76.53  49,23 
77,3849,77 
78,22 

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82. 40  < 3, 0.12 

83,2653.56 


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52 
53 
54 
5,5 
56 
57 
58 
59 

67 

60 

63 
64 

65 
66 
67 
68 
69 

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72 
73 
74 
75 
76 
77 
78 

79 

^o 

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82 

83 

84 


86 
87 
88 
89 
90 


92 
93 
94 
95 
96 

97 
98 
99 


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68 

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6  c 

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1.64 

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3,27 

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3,31 

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6 

7 

5,8 

381 

5,85 

3.84 

5,84 

3,86 

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7 

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6,7:J 

4,36 

6,69 

4,39 

6,67 

4,42 

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4,90 

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4,93 

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11,71 

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7,73 

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8.22 

12,5 

8,28 

12,4 

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15 

16 

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8,77 

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8,83 

13,30 

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17 

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9,26 

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14,18 

9,38 

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17,61 

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11.51 

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21 

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1,98 

18,4 

12,    6 

18,35 

12,14 

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22 

23 

2,53 

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19,18 

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13,16 

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13.25 

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27 

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22,51 

14,90 

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15,45 

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2.9 

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24,18 

16,01 

24,11 

16,11 

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6,34 

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29,19 

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6.67 

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54-36 

3,5,64 

54,20 

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36,0 

65 

66 

55-3? 

35,95 

55,19 

36,19 

55-°4 

54,88 

36,67 

66 

67 

56,19 

36,4.9 

56,03 

36,74 

55,87 

36,98 

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37.04 

56,87 

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57,87 

37,58 

57,7- 

37,83 

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57,37 

38,33 

69 

72 

58,71 

38,12 

58,54 

38.38 

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62,72 

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63,56 

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42,22 

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64,58141  94 

64,39 

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42,50 

64,02 

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77 

78:65,42142,48 

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43,33 

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82 

83 

69,61 

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83 

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70,05 

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48,02 
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74,4348,80 

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TRAVERSE     T  A  B  L  E. 


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TRAVERSE     TABLE. 


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21,62 

30.84 

22,20 

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4.5,73 

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45.59 

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52,43 

36,71 

52,27 

36,91 

52,10 

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51,94 

37,39 

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37,28 

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38,09 

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55.70 

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55,53 

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61,25 

43,29 

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60,87 

43,8. 

75 

76 

62,26 

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43,86 

61,87 

44.13 

61,68 

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76 

77 

63,07 

44,17 

62,88 

44,44 

62,69 

44,  71 

62,49 

44,99 

77 

78 

63,89 

44,74 

63,70 

45,o* 

63,5° 

45>29 

63,3° 

45,57 

78 

79 

64,71 

45,  31 

64,5' 

45-59  | 

64,32 

45,88 

64,11 

16,16 

79 

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6,5.53 

45,89 

6/5.3  a 

46,17 

65.1-5 

46.46 

64.0^ 

46.74 

80 

81 

66,35 

46,46 

66,15 

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47i°4 

65,74 

47,32 

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82 

67,17 

47»°3 

66,96 

47,33 

66,  r  6 

47,62 

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82 

83 

6;,99 

47,61 

67,78 

47,9° 

67,57 

48,20 

67,86 

4«,49 

83 

84 

68,81 

48,18 

68,60 

48,48 

68,39 

18,78 

68,17 

84 

69,63 

48,75 

69,41 

49,06 

6>.20 

49»36 

68,9^ 

49,66 

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86 

70,45 

49,33 

70,23 

49,63 

70,01 

49,94 

69,8, 

50,2^ 

86 

87 

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49,  9°  1 

7i,05 

50,21 

70,83 

5°  52 

7Q,  61 

0,83 

87 

88 

72,09 

50,47 

71,86 

5o,79 

71,64 

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71,42 

i,41 

88    1 

89 

72,90 

5  '  ,05 

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51,37 

72,46 

51,68 

71,23 

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89 

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73,72 

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73-27 

52.26 

73-04 

2,58 

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75.36 

52,77 

75,13 

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76,18 

53,34 

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53,67 

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78,64 

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20,1014,87 

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29,6; 

22,14 

37 

38. 

3°>74 

22,34 

30,64 

22,47 

30.5522,60 

3()>45 

22,74 

38 

39 

31,55 

22,92 

31-45 

23  06 

31,3523,20 

•51,25 

V3,33 

39 

32»36 

23-51 

32.26 

23.65 

0,2.1523,79. 

32.05 

4i  .., 

33.1724,10 
33,9824.69 

33^7 

24,^3 

3*,96 
33.76 

M,39- 
24,98 

32,^5 
33,d5 

25,13 

4i 
42 

43 

34,79 

25,37 

34,68 

25-43 

34,57 

25,58 

34^45 

25-73 

43 

44 

35,  6^ 

2,,  86 

•35,4$ 

26,02 

35,37 

26-17 

35,26 

44 

45 

3641 

2645 

36,29 

26,61 

26,77 

36,o( 

26,92 

45 

46 

37,1° 

27,20 

36^98 

27,36 

36,86 

27,  5a 

46 

47 

38^0227,63 

37,9° 

•>7,79 

37»78 

27,96 

37,66 

28.12 

47 

48 

38,83*8,21 

38,7' 

28,08 

38,59 

28,55 

28,72 

48 

49 

09,6428,80 

39,52 

28,97 

39,39 

£9,15 

39,  *t 

29,32 

49 

_5°_ 

40,4,5  29.39 

40,32 

40.1929,74 

4<',o6 

29,92 

i  c: 

Uep.iLat. 

Pep,  L.a't. 

D-p.  La  . 

l>;i.. 

Lar. 

«   ^ 

3 

54    Deg. 

53  1    Deg. 

53fT5eg; 

53^   l)eg' 

'^ 

TRAVERSE     T  A  U  L  E.                >5 

36   De*.    ||    36!   Oegk 

36*  Deg. 

?61  DeR. 

y.  r- 

•  P 

Lai. 

Uep.  |j|  La-.    L»r-n. 

L,at. 

)eo. 

J-,ai. 

O«-p. 

~3    *• 

5' 

41,26 

29,9*  ||  4M3 

30,16 

41,00 

3o,34 

40,80 

30,5  ! 

51 

52 

42,07 

30,56  |  4i,94 

30,75 

41,8- 

30,93 

41,67 

3  1,11 

52 

53 

42,88 

3M5 

42,74 

3i,34 

42,60 

S'jSS 

4«f47 

3^71 

53 

54 

43,69 

3»,74 

43,55 

31,93 

43,4' 

32,12 

43,27 

32,31 

54 

55 

44,5* 

32,33 

44,3 

32.52 

'44,21 

32,71 

44,07 

32.91 

55 

.56 

45,3° 

32,92 

45>if 

33,  'i 

45,o? 

33,31 

44.87 

33,51 

56 

57 

46,11 

33,5° 

45,97 

33.7o 

45-82 

33,9^ 

45.67 

34>10 

57 

5'8 

46,92 

34,09 

-46,77 

34,3o 

46,69 

34,5? 

46,47 

34,70 

58 

59 

47,73 

34,68 

47,58 

34,89 

47,43 

3>j,09 

47»27 

35,  3° 

59 

60 

4*-54 

35-27 

48.39 

35-48 

48.23 

35-69 

48,08 

35,90 

60 

61 

49.35 

35,85 

49,  if 

3607 

49,°4 

36,28 

48,88 

36  50 

61 

62 

.50,16 

36,44 

50,00 

36,66 

49,84 

36,88 

49,68 

37,io 

69. 

643 

50,97 

37,03 
37,62 

50,81 
51,61 

37.25 
37,84 

•5M< 

37>47 
38.07 

50.4837,69 
51.28*38,29 

64 

65 

52,59 

52;42 

38,44 

52,2? 

3S66 

•52,0813^8.9 

65 

66 

•53,4° 

38,79 

53,23 

39,03 

53,05 

39.26 

52,88]39,49 

66 

67 

.54,2- 

39,38 

54,03 

39,62 

53,86 

89,85 

53,68 

40.09 

67 

68 

55,01 

39,97 

54,84 

40,21 

54,66 

4o,45 

54,49 

40,69 

68 

69 

55.82 

40.56 

55:  M 

40,80 

55,47 

41,04 

55-^9 

4r,28 

69 

70 

50,63 

4f,i4 

56,45 

41-39 

."16.27 

41.64 

70 

71 

57,44 

4i,73 

57,26 

41,98 

57,()7 

42,23 

56,8942,48 

7i 

72 

,58,25 

42,32 

58,06 

42,57 

A7>88 

42,83 

57,6943,08 

72. 

73' 

59,06 

42-,9i 

58,87 

43,17 

,58,68 

43  4* 

5.8,49 

43,68 

73 

74 

59,87 

43,5° 

59,68 

13,76 

59:49 

44,02 

59,  -9 

4-4-28 

74 

75 

60,68 

44,08 

6  >,4^ 

44,35 

60,59 

60.0944,87 

75 

76 

61.49 

44,67 

'61,29 

44.94 

"61,09 

4.5,21 

6<>,9<>l45,47 

76 

77 

^2.29 

15  26 

62,10 

45-53 

61,90 

45:8? 

61,  70146,  07 

77 

78 

63,10 

45,85 

62,90 

46,  1  2 

62,7, 

46,40 

62,50146,67 

79 

8_ 

03,9' 

£4-,  70 

46.43 
47,02 

63,7' 

47-30 

63,5 
64.31 

46,99 

63.30147,27179 
;64,io'47.87  «o 

81 

<>5,53 

47  61 

65,3* 

47,9° 

65  ,  i  1 

4«;i8 

64,90  48-  46  61'  I 

82 

48,20  | 

66,13 

.8,49 

65,9^ 

48,78 

'65,7049,06;  82    I 

83 

b7,i5 

48,'7Q 

66,93 

f9,o8 

66,  72 

49,37 

66,50 

49,66|  83 

84 

67,96 

67,74 

49,67 

6/;52 

19,97 

67,31 

60,26j   84 

85 

68,77 

49,96 

68,55 

50,26 

68,33 

50,56 

68.!  j 

50,86'  85 

86 

69,58 

50.55 

69:35 

50,85 

69,!3 

51,  J5 

68.  91*51,  46 

86 

87 

70,38 

51,14 

7°,  M> 

69,94 

5',  75 

69,7  '[52,05 

87   ( 

88 

7M9 

5J,73 

70,97 

52,04 

7°,74 

5Z«34 

70.515^,65 

88 

89 

72,00 

52,63 

7  1  '54 

52,94 

7^3' 

53:25 

89 

9° 

vp..8i 

51.90 

72.58 

53,22 

•72  3"; 

53,53 

72,11 

53,85 

9° 

9i 

73,62 

53,49 

73,39 

53.  81 

73,15^ 

54,  '3 

72,91 

54,45  91 

92 

74-43 

54,°8 

.74-H' 

54.4° 

73,95 

54,72 

73,72 

55,05  92 

93 

75,a4 

54,66 

.75.00 

54-99 

74w6 

55-32 

74,52 

55,64!  93 

94 
95 

76,05 
76,86 

55,25 
55,84 

76,61 

55.58 

75:56 
76.37 

55,9' 
56,51 

75,32 
76,12 

56,14  94 
56,84!  95 

•   96 

77,67 

56-43 

77,4^ 

56,77 

77,17 

57,10 

76,92 

57,44)  96 

97 

78,47 

57.°fi 

78,20 

57,36 

77,97 

57-,7o  1 

77,72 

^8,04'  97 

98 

/.9,a« 

57,6o 

79  >°  3 

78,78 

18,29 

78^2 

58,64-98  | 

99 

S  >,C9 

58-.  1  9 

79,84 

.8,54 

79,58 

58.89 

79,32 

!9,23!  99 

loo 

80,90 

58.78 

80.64 

80.30 

9.48 

8".  13 

59.831,00  I 

1  <=' 

Dcp. 

..at. 

Uep. 

,ar. 

Uep. 

^at. 

*"  *r 

b 

54  l>g. 

53  J   Deg> 

5  3i  ifcg- 

53!  Deg. 

a  q 

76          T  £  A  V  E  R 

%.te*-^-~^-^*=< 
EtC 


S  E    TABLE. 


I;'* 


37i_^Sl    5  Q 
L,t.    bep     r3   # 


T  R  A  V  E  R  S  E    T  A  B  L  E. 


ft.Gft&£! 


,a  .    U 


51 

52 

5342,33 
54 


5644,7* 
fi 


5947,12 


51  90 
32  5° 


d,/u 
34,3' 
34  9  * 
3..S-51 


6'249,5*37-3r 
6350.31137.91 

65J51, 9 »  S9  I2 

66J52, 713^7- 
671535*4     3 
6o!5453i:4    92 
6955-- 


Lat^ 

40,60 

4t,393i 


43 
44  5  5 
45,37 
46,17 
4  6  .-96 
47-76 


7833 


S5t>36 


49=33 


51,74 

53:   :- 

54 


?!    ?.     P.  o 
•  ^J92 

I!  55JJJ 

,36,70,.,-  ;l     i2,9« 

57»3'» 


73|5«^ 
74!59; 


[43,93 

53 


75*59,9' '45, 14 

76|6i',7o45,74, 
77;6vi9i46,34 
7862,2946,94 


54 


59,7 
60 


32,08 

32,6? 

,29 


34-5° 


36   92 


,92 

37,53 
38,13 
943*?74 


39.- 3  4 
39-95 


3  i". 
134*: 


5046 


44,79 
4  5,4  • 
'  oo 


fc^SgWku   |6_3±ll 

8i64,69|4::'75 

8265,49149,35 

83:66,C949,95 
8|'67,o9!5o,s5 

8V6;,B8J5«,i5 
8(>:63,685i,76 
8769,4^52,36 
8870,28152  96 

8tf7«t*:?g3»5« 


62,09:47,21 

62,0847,8* 

63.  o^4S,4<! 

&i}4BJ49,o3 
65,27'49;63 
66.0750,24 
66,86150,84 

67,66151,4? 


8 


loo 


==^^s^ 


Lai. 
40,4^ 


4^,°'- 
42,84 
4^.63 
44-43 
45- a  a 
46,0  t 
46,81 
47.60 


Up.  I)  Lat. 


}2,26 


34,09 
34*7<- 


49,'9!37i74 


J39-57 


53,95J4-40 
54,74|42,oo 

5&,;j3|43.2-2 
5-,»»43.^ 
57,9'  4-1  -44 
53,7145  05 
59,5  '45-66 
,2946.2; 

S^aA*? 

r    "    47,4« 

62,67 

3d748/ 
6},26 
6-5.95 


66,64 
67:43 


69,82 
70,61 

liill- 

72,99 
73,/8 
74>5r 
75,3" 

7696 

77,75 
7^,54 
Till' 


49,3i 
49^9* 
5°  53 
r)',i4 
•51,74 

52  96 

53,57 


5,5 


59- °5 

.i9»6«> 

60,27 

60,88 
L^T 


41.12 

4-7 


I5,f  7 

46A< 
47,44 
48.23 
49  02 


5 1,3'. 
52. 19 

5~,9- 
53-7' 
54-5^ 


5^>:9' 

57,7-' 

5v-3- 
60  .'•  i. 

6^67 

62,4f. 

6*M. 


b-l,°5 

64,84 

60,40 
67,21 

68!7«, 
70,37 


72,7^ 
73,5i: 

74-3^ 

7SM2 

75;9 
76,7 

77-4' 


L), 


Dep 


33-6- 
34,28 

34,9' 

;i5-5! 


37  35 
37,9C 

39, 4  8 

39,79 

;i,o* 

42,2.1 


43  47 


1 7, 75 
l:^,37 


19,59 
JojSi 


53,2< 
535S^ 

J4,49 
•^  .ic. 


60,61 


V  E  R  SE     T  A  B  L  E. 


J)eg 


i^j  . 

0,71 

^57 

s'»3 

3r9' 

4,7° 
5,4^ 
6,26 

7>°4 
7.8- 

8.61 

9,39 
10,17 
10,96 

12,52 

13,3 
14.09 

14,87 


17,22 
.8,0, 

18,78 
'9-5; 


20,3^ 


J:p. 


i  87 


3,74 


5.6- 
6  90 

0.05 

747 
8,09 

8,72 

9,34 

9,96 

10,58 

11,21 

12.45 
13,^7 

14.32 

»4;,94 
16,19 


16,81 

2I,9»1 

22,70J!8,05 


23.48 

34,26 

*s8f 
26. 6r 


28.96 
29,74 

r.3 


32,09 
3*,87 
33-6,3 

34,43 


ill0. 
25. 
26-15 
26,77 

28'oi 

_  ..    19*6 

37»57  J9»88 
38,3.5  3()-5° 

39<       . s 

H  Dq^Lat. 

S 


18.68 


19,92 


22,41 

23,03 
-3,66 


*G*. 


L 


3  Jv 

3,9- 
4,68 

5,4 

6.24 

7,o 


9-3 


4.04 


1638 
17,16 

i?$ 

»6V»8 

2!  06 
21,84 
22,62 

2r-*  4 
«4,»« 


26,52 

28,08 

28,8( 
29,64 


33^53 
35,09 

36,65 

37.4 
38,21 


1,88 

s!i3 
3.76 

4,3* 
5,oi 

5,63 
6,26 


7,5J 
8.1, 

8,76 
9-39 

10,0] 

D,64 

il,27 
11,85 


3,7 
«4,4< 
o  * 

15,65 

16,27 

16,90 

17-53 

1 

18,78 


9 
10 

1 1 

12 
13 

M 
'5 
16 

17 
18 

20 

22 
23 
24 

:i 

27 
28 
29 


M» 
$5 


3i 

32 
33 
34 
35 

3  36 
37 
38 
39 

'4  _1L> 


•41 


6 


z6, 


50 


4i 

29  42 
91  43 
54  44 

«7'45 
79  46 
42  47 
jQ4  48 
'67  49  H 

-52   i 


at 


s«i 


l>eg.    Q^^ 
===ii4O^i 


T  R  A  V  E  R  S  E    TABLE. 


De*. 


^*#D3* 


Lar. 


39,7; 

42-,  1 1 
42,89 
43,67 

45,23 
46,01 


47 
48:3 


49,9' 
5"> 


69  4 


53» 


31,92 
32,55 
33.17 
33,8o 

34,43 


35,68 
36,30 
36,93 


4,6jL79  iL£§  i: 


57-38, 


,18  61 
38>8ij  62 
49,1339,43!  63 
»i-6.  64 
0,68  65 
66 


41,94 


67 


68 
43,19'  69 


55'37|44-44i 
56,1545,07 
56,9.^5,69 
57,7*  4A3* 
5^,49!46,94j 
59,2747,57; 

60,0548  20! 

6i,6iJ49»45 
62. 30*50,07! 

63  -1715°,  7«> 
63,955I-.33 

65,5115^,58 
66,29;53,H 
67,0753,83' 
67,8554,46 
63, 6355^8 

69,4! 


7i 

72 
73 

74 

75 

77 
78 

79 
Xo 

«i 
82 

83 

84 

85 

86 

88 
89 

7'>»'956;33!  9_* 
70,97 


7 ',75 
72,53 


*za 


56,96 

57,58 

58,21 

58,84! 

74,09^9,46: 
74,87160.09 


,7il  97 


76,4361,34; 


77^162,59 

Dep.lLlt. 


99 

Oo 

T  \t 

«S3 

S 

^•& 


So 


T  RAVERS  K    T  A  B  L  E. 

*'&&   MMVMBMI     TirarauMi   •  •  **m  IBUIJI  ^'•'X*ato9m^*mm*mu*l^amrr*v**>mmm  .-••«>  VT^VM^WW^KS^^U 


^  •— '     3X       ^V6*      £|     ^WJ."V'6*          3^2         W6'          J^t.    j    "o* 


TRAVERSE    T  A  B  L  E. 


5643,52 

5744,3V 
5845»07 
59i45,8537,i3 

60146.^137.76 

6'|47,  _ 
6248,18139,02 

6348,9639,65 
6449,7440,28 

655.0,51  4a,9! 
6651,2941,54 
6752,0742,16 

6852,8542,79 
6953.5*43542 
70154^40  44,05 
7i55'i844, 68 
7255,9545,31 
7356,73<45,94 

'-y^'C'7    Cllln,./**? 


76,59,°6.47,83. 

77;59,84'48,46 


8263,735x,6o 
83  64,5°  52, 23 
84165*2852,86 
gi5|66,o6|53,49 
86166,8354,12 
^767,6I54,75 

1 -.!_,     n<f 


51, 


54-^1 


4B,39 


52,66^ 

53,4343,66 


44-20 


54,9844,92- 
55,7645,55 

56,5346,19 
46,82 
58,0847,45 
58,85148,09 
59,63148,72 
60.40149,3; 
6i,i8J49,98 
6i,Q/v.v*,6a 


63,5051,8* 
64,27152.51 
63. 05^53,15 


66,6oJ54,4i 
6/,3755,0? 
68,15  55,6$ 
68,92*56,32 


'4  5^  2 1 

72,0258,84 
72.7959,47 
73;576o.ii 
74,3460,74 
75,i-;6i,37 
75,89562,01 
76,66562,6; 
77-4IJ63;5? 
Dep.'Lat. 

5^* 


.9341.98 
5',  7°  4V 
5^,4743.25 
53.24*43.89 

54-°  •'.  -14,53 
5-i,7^45>I6r 
55^6  45,8<> 

56,3346,43 


&7.>*7  tf, 71 
58,6448,34 
59,42  4S.9» 
6  J,  19  49,61 
0^,96  50,25 
61,7350,89 
62, 5°  5 1,5  2 
63,2752,16 
64,0451,79 
64,82  53,43 
6s ,59  54,07 
66,3654,70 

67,!3 J5  34 

67-90 

68,67 

69,45 

70,22 


54-50 
55,3^ 
56,13 
56,89 
57,6(- 
5B,4S 
59,a- 

59^97 
60. 


44 


15=4 


47,96 
48,6, 
49,2, 
49;8i 


7i 
72 

73 
74 
75 
76 
77 
78 

79 
8> 


s* 
&.c»» 


TRAVERSE     TABLE. 


i 

2 

3 
4 
5 
6 

8 

9 

10 

ii 
(2 
13 
H 
15 
16 

17 
18 

19 

20 

21 
22 

23 
24 

2? 
26 

27 
28 
29 


32 

33 
34 
35 
36 
37 
38 
39 
-1- 
41 
42 


40  Peg. 

Lat.  Dep. 
0,64 
1,29 
r,93 
2,57 


I.-53 


5,36 

6,13 
6,89 
7.66 

8,43 
9>'9 
9»96 

ri,49 


75  07 


9,00 
9564 


12,2610,28 
13,02^0,93 

3-79  n,57 
4,55)12,21 
12,86 


16,09 


14-14 
14,78 
8>39  15,43 
16,07 
16,71 


43 


20,68 
21,4518,00 

22,2218,64 

22,  98)19, V* 

23'75JI9  93 
24,51! 


25,2821,21 
26,05 


26,81 

27.5 

28,34 

29,11 

29,88 

30,6 


22,50 

«3»78 

24,43 


0,76 


3,° 

3,82 


6,n 

6,87 
Zi?3 
8,4 
9,16 

10,69 

11,45 
12,21 


0,65 
£58 

3,23 


5,Sa 

7,n 

7,75 

9*°5 
9,69 

Io,34 
10,9* 

13,74  n:63 
14.502.28 
15^2612.92 
16,0313,57 
16,7914,21 


18,3 

19,08 

19,84 

20,6 

22,13 
22,90 

23,66 
24,42 
25, '9 
25,95 
26,71 

27,48 

28,24 

29^00 


15,51 
16,15 
16,3 » 

!7,45. 
18,09 

18.74 
19.38 


20,03 

20  6.3 
21,32 
,41.97 
22,6l 
23,26 


9,74 
12,17 

12  93'iiio4 
13,69:11,69 

£5_L2j'i2.99 
i6;73|U-29 


/'Tt7        A?.yA 

18,25^5,59 
19,01116,24 


20,5317,54 
2i,29|i8,i8 
22,05118,83 
22.81  19.48 

23  57|2>,i3 

24.3'.jjiO.7'a 

25,o9J>Ji,43 
25,8522,08 
26,61  22,73 
^7,3723,38 


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243 
255° 


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Lit.    L) 

0,7C 


2,2 
3-0? 

3,?c 

5:3* 

6, of 
6.8c 

7>5J- 

«,3'- 
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9,8, 


l606; 


a°:4c 
21.2) 

21,97 


0,65 

i-96 

2,6j 

3.26 

3  9s 
4<57 

5'J7 


7,;^3 
8.49 

9^79 
10,44 
ii, i 

1 1,7,5 
12,40 
13  06 


15   Ql 

15,67 
l6,32 

l6,97 
17.62 
l8,28 


TRAVERSE     T  A  B  L  E. 


.83 


«RUV 

^  °. 

40    De<7. 

40  I       0--. 

ooj   Deg. 

..._._.  ......... 

f  r3 

Lar. 

L>ep. 

La    . 

> 

La 

i>e*\ 

Lf 

O-n. 

*    e 

—  ~ 

39,07 

32,78 

38.9'..' 

3^95 

38.7fc' 

|3.ia 

3^64 

33,29 

51 

5"- 

i9  83 

33,42 

39  fe 

53,60 

3.9>M 

'J3*77 

39;  39 

33,94 

52 

53 

*(>,€ 

34,07 

4  >  ,  /A  ^ 

H-a4 

40,3 

34,42 

40,15 

34,6o 

53 

54 

41,3; 

34,71 

41,21 

34,89 

41,06 

35/J7 

40,91 

35,25 

54 

55 

42,13 

35,35 

41,98 

3.5-54 

41,82 

35,  7  2 

41,67 

35,9° 

55 

56 

42,90 

36,00 

42.74 

36  18 

42,  5b 

36,37 

42.4^ 

36,?5 

56 

57 

13,66 

36,64 

43-5 

36,83 

43,34 

3  7,-  '2 

43,18 

37,  »» 

37 

5? 

44«43 

37,28 

44^7 

57,48 

44,1' 

37,67 

43,94 

37,86 

58 

59 

45,  2c 

3.7,9* 

45,-,  93 

38,12 

44,86 

3  ,32 

44,7° 

3^,51 

59 

6^ 

15.06 

45,". 

38.77 

4,5-6" 

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45-45 

39,17 

61 

+6.73 

39:  *l 

46£Jfc 

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40^8 

39,62 

46,21 

39,82 

67 

62 

17,49 

39-85 

47-32 

40,06 

47,15 

40,27 

46*97)^0,47 

62 

6.3 

48,26 

48,08 

40,71 

47,9' 

40,92 

47,73j4i,n> 

63 

64 

10,03 

4M4 

48.  8  « 

4l»35 

48.67 

41-  56 

4.8,4841,78 

64 

65 

4-9,79 

41,78 

4.9  61 

42,()o 

49,43 

42,21 

49,2442.43 

65 

66 

50,56 

42,42 

5o  37 

42,64 

5°,i«; 

42,86 

5^,0043,08 

66 

67 

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43-07 

51,14 

13  <29 

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50,76 

43,73 

67 

68 

52,oo 

43;  7  I 

5I,9G 

43,94 

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44,16 

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44-39 

68 

69 

52,86 

52,66 

44,53 

5*,  47 

44,8i 

52,27:45,04 

69 

70 

53,62 

45,0° 

5-lll3 

45,23 

53,23 

4^.46 

5  3  »°  3  4  5,  6  9 

70 

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54,39 

45.64 

54,19 

45-87 

53,99 

46,  =  1 

53>79i46,35 

71 

55,16 

46,28 

54-95 

54,75 

46,76 

54,5447,°° 

72 

73 

55,92 

46,92 

55,7* 

47,'i? 

55,5^ 

47-4' 

55,30347,65 

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74 

56.69 

47,57 

56,  48 

47,  §i 

56,27 

48,06 

56,06^8,30 

74 

75 

57,45 

57.24 

^8,4^ 

57,03 

48,71 

56,82^8,96 

75 

76 

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4^85 

58,01 

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£7,79 

49,36 

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76 

77 

58,99 

49,49 

58,77 

i9,75 

58,55 

50,01 

58,3350,26 

77 

78 

.59,75 

59-53 

5^,4° 

59,3! 

50,66 

59,°9!5°,9^ 

78 

79 

60,52 

50'  7  8 

65,30 

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60,07 

51.31 

59,85  51.57 

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51.42 

61,06 

,-1.69 

60.8-3 

5  "'-96 

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80 

81 

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52,6, 

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81 

83 

62,82 

62,59 

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53,^5 

62,1213,53 

82 

83 

63,58 

53,35 

63,35 

5.^63 

63,11 

53,90 

62.8.^54,18 

83 

84 

53$99 

64,11 

54  27 

63,87 

54-55 

63,641,54,83 

8.4 

65,11 

54,64 

64,87 

64,63 

64,30 

55,48 

85 

86 

6.5,88 

65,64 

55,57 

65,39 

55,85 

65,15 

56,14 

86 

87 

66,65 

55>9* 

56,21 

66,16 

56,5° 

65,  Q  I 

56,79 

87 

88 

67,41 

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66,92 

57,15 

66,67 

57,44 

88 

89 

68,18 

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67,93 

5^,5° 

67.68 

57,8o 

67,42 

8y 

92 

68.01 

57,8j 

68,60 

58,1.5 

<>8-44 

58^45 

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58J75 

91 

69,  7  > 

58.49 

69  45 

58,80 

69.20 

59,10 

^8,94 

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91 

92 

70,4* 

59,14 

70,2V 

59,44 

69,96 

5.9,75 

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60,0^ 

92 

93 

71,24 

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7^,9* 

60,09 

"70,72 

60,4  > 

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6-),  7; 

93 

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72,01 

60,  4  z 

71,74 

60,74 

71  48 

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71,21 

61,36 

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95 

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72.51 

Si,  38 

72,24 

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7',97 

62,01 

95 

96 

73,54 

61,71 

73,27 

62.03 

73,°° 

t)2,3.5 

72,73 

62,66 

96 

97 

74,3' 

62,35 

74  -09 

02^67 

73,76 

63.00 

73,48 

63-3^ 

97   1 

75»°7 

62,99 

63,32 

74-52 

63,65 

74,  *4 

63,97 

98   | 

99 

75,84 

63,64 

75,56 

^3,97 

75,28 

'M,3  ' 

75,  °' 

64.62 

99 

loo 

76,6- 

64.28 

76,  3  v 

76.04 

64,04 

75-7^ 

65,28 

,00 

26  <== 

Dcp. 

t  at. 

Uep. 

HaTT 

Deo. 

Lat, 

Dep.Lat. 

-"S     «a 

51 

50  Deg. 

40!   Deg. 

49*-  Deg. 

49T  ^e?- 

o  r' 

&2S 

^'% 

w& 


11 Q  49 
tfSaMn— 


48  £  Deg.  § 

==:W7  »^S  ^ 


^TRAVERSE    TABLE.             8 

*v*.VA 

4  1   Deg. 

41  Ml-.    |,    4i,|  Dee. 

41?  Deg    0  f 

t     —  - 

La  . 

O 

Lat, 

L>?u.{|Lai. 

L)»P- 

Lat. 

iJ-p 

P 

51 

3*,4S 

33,46 

38,34 

33,  -3 

38,2r 

33,79 

38.0 

33  ^ 

51 

52 

39,  «4 

.4,12 

39.10 

34,29 

3%>9e 

34,46 

38,7 

34.6^ 

5^ 

5'3 

40,0, 

34,77 

39& 

34,95 

39,6c 

35,i2 

39-5 

35;2S 

53 

54 

40.75 

3543 

4^,60 

35-6o 

40,4^ 

35,7^ 

40,2 

JtS  »9^ 

54 

4I»51 

36,08 

4i,35 

36,26 

^6,44 

41,0 

36,6, 

55 

5642,26 

36,74 

42.10 

36,92 

41,9^ 

37»ii 

41,78 

37,2(5 

56 

37-4° 

42,85 

37.58 

42,69 

37,77 

42,53 

j7,9t 

57 

5%8v77  38,05 

43,6i  38,14 

43,44 

3^,43 

43»2- 

.58,62 

58 

44  36 

3^,9° 

44-19 

39,09 

44,02 

39,29 

$ 

6o!45!a8  .W36 

47,11 

,^•56 

44,94 

39  76 

liiZl 

39,95 

"** 

61  46.0440,02 

4^  8." 

45,  6y 

40,42 

45,5 

40,62 

61 

62  -46,79  4°»68 

46,61 

40,'S8 

46,4441.08 

46,26 

41,28 

62 

63:47,5514  *'33 

47-37 

4^54 

47,i»  41,  75 

47,oo 

41>9,'j 

63 

6448,304'  9-) 

4$,ia 

42,20 

47,93142,41 

47  7J 

42,C»a 

64 

65 

40,0642,64 

48.2:7 

42,86 

48,68)43,07 

48.41 

43,28 

6.5 

66 

49,8  1  ;43  .3° 

49,62 

43,5* 

49,4343-73 

49,2: 

43.9 

66 

67 

5',  37 

44,18 

50,18 

44,40 

49»99 

44,61 

67 

68 

51,3244,61 

51,13 

44,24 

50,93 

50,7 

15,28 

68 

69 

52,0745.^7 

51,88 

45,49 

5  ',68 

45,  72 

51,48 

45,95 

69 

7 

52,83;45,92 

52.63 

46  .15 

52,43 

46.38 

52,22 

46.6. 

7l 

53.5846,58 

53,38 

46  8. 

53,i8 

47,05 

52,^7 

17,2» 

71 

T8 

54,34;47»24 

54,13 

47,47 

53,92 

47,7J 

53,7^ 

47,94 

72 

73 

55*'  9  47,89 

54,88 

48,13 

54,67 

48,37 

54.46 

48,61 

73 

74 

55>85;48,55 

55,64 

48,79 

55,42 

49,l!3 

55,  21 

49,28 

74 

75 

56,6049,10 

56,39 

49,45 

56,17 

49,7° 

55,95 

49,94 

75 

76 

57,3649,86 

57*^ 

56,92 

50>36 

56,7 

50,61 

76 

77 

58,1150,52 

57,89 

50,77 

.57,67 

51,02 

57,45 

51,27 

77 

78 

58,8751,17 

58,64 

5i  43 

58,42 

5i,68 

58,1^ 

5^94 

78 

79 

59,62,51,83 

59>4 

52.09 

59,17 

5*r35 

5^,94 

59.6 

79 

8  |6.>,38i52,48 

60.  ir, 

52,7? 

59,9*. 

5  '^  ,  o  i 

59.  6H 

53.1? 

8  > 

81 

6',  1  3*53  '4 

60,90^  3  ,4  1 

6  ,67 

53^7 

6>,43 

53,94 

81 

82 

61,89:53,80 

61,65154,07 

61,41 

54»33 

61,18 

o4,6o 

82 

8463,4055,11 
8564,15:55,76 

62,4 

63,15 
63,9! 

54,73 

56,04 

62,16 
62.91 

63,66 

55  °° 
55,66 
56,32 

61,92 
62,67 
63,41 

36,'  6c 

CO  rf<  >.C 
OO  OO  OO 

8664.9° 

56,42 

64,66 

56,70 

64,41 

56'99 

64,16 

7,27 

86 

87)65,66 

57^08 

65,4* 

57,36 

65,16 

97,93 

87 

88'66,4ii57,73 

66,  1  6 

58,02 

63,91 

i8,3i 

65^65 

8,60 

88 

89:67,1758,39 

66,91 

58,68 

66,(56 

58.97 

66,4q 

9,26 

89 

9    67.92 

59,05. 

67^67 

59,34 

67.41 

67,15 

9,93 

90 

9168,68 

59,7' 

68,42 

60,  co 

68.1560,30 

07,89 

>,6 

yi 

92 

69,43 

60,36 

69,17 

00,66 

68,90 

60,96 

68,64 

1,26 

92 

93 

70,19 

61,  oi 

69,9- 

61,32 

69,65 

61,62 

69,38 

1^93 

93 

94 

70,94 

61,67 

70,67 

61,98 

70,40 

62,29 

70,13 

2,5/ 

94 

95 

71,70 

62,33 

71,42 

60,64 

7i,i5 

62,95 

7o,8« 

3,*^' 

95 

96 

72,45 

62,98 

72,18 

63,3° 

71,90 

63,61 

71,62 

3:9^ 

96 

97 

73,2i 

63,64 

."2,93 

63,96 

72,65 

64,27 

7^,37 

4,59 

97 

98 

73,<X> 

64,29 

73,68 

64,62 

64,94 

73," 

5,26 

98 

99 

74,72 

64,^5 

74,43 

65,28 

74>35 

$           S* 

55,60 

73,86 

5.92 

99 

100 

75,47 

6,5.61 

75,1865,93 

74.90 

56  26 

74.61 

6,59 

oo 

:      -N-* 

U>cpJ 

L<H. 

Dep.lLat. 

Lat.  , 

Dcp. 

^at. 

3"  j 

"5  Q    49  Deg. 

48  J  Deg. 

4-81  Deg. 

48  l  Dee. 

"5  & 

#£* 

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ABLE. 


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as        T  R 

2&.<>T&*^= 

O     43  & 


AVERSE    TABLE. 


12 


5<is 

5-8- 


8,04 
8,78 


•2,43 


0-6' 

65OC 

6,82 

7,55 
8,28 
9,0. 


1,21 


2567 
3,4 

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j.6« 
136 

2,05 
2,73 


4,77 

6,14 
6,82 

8.' 1 8 
8'.87 

9,55 


2,28 


6»33 
7 


7-79^5 


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999 
0,72 

i  45 
1,18. 


19,10 


-1,14 


22,51 
23,T9 


26,60 

27,28 
^7,96 
18,64 

30,01 

30,69 


Lat      DeP. 

0,69 
i,37 


4,37 


7.28 


9,47 
10,2 

11,65 
12,38 
13,H 


2-74 
3,43 
4,11 
4,8o 
5,48 
6,17 
6,8  > 


7.54 

8,22 
8,91 
9'59 

10,96 

12*33 

3,f>2 


i5,75 
17  4 


19.6; 


^6,9.5 

27,6 
28,41 


29,80 
3°559 

32, o;, 


14,39 

«5>°7 
15^6 


17, 8» 
18  50 
19,19 
19.87 


23,3' 
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i6,o4 


£0.09 

29,46 


jo,8a 

3i?52 

34,23  32,20 


431 


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3,6 
4'3. 
5»° 
5,8 

6,5 


8,7 

10,  i 
10,8 
11,6 

12»3 

13,06 


'5,9 


18,86 


21,04 
21,76 

22, 49 

23,21 


24,6,x 

25,39 

26,11 

26,8 
27,56 
28,29 
29,01 


32,64 

33  37 
34-% 
34,8* 

35,51 
36-2; 


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0.69 
1,38 

2.07 

3»44 

t&2 

5,51 
6,90 

6,88 

8^26 
8,95 


11,7° 


3  7? 


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1790 

9,27 

9  96 

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2^34 

22,72 

2340 

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4.78 

6'i6 
6,85 
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8,22 

8,91 
9,60 

o'98 


3>°4 
3>73 
4.42 


46^  Deg. 


4iL 

Deg. 

o,7s 

0.69 

1,38 

2,1- 

3,07 

2,89 

2.77 

3,6l 

3>46 

4,33 

4-»5 

5»o6 

4,84 

5,78 

5>53 

6,5 

6,22 

7.9.- 

6.09. 

7,95 

761 

9»39 

8J99 

10,1 

9.68 

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£«>76 

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12,45 

13,72 

13,1* 

13.83 

1  6,'  6 

'5,90 

17,3: 

16,60 

i8,o< 

17  20 

18,78 

17^98 

19,50 

18,67 

20,23 

19-36 

zo  9^ 

20,05 

2K6^ 

»°»75 

22,39 

21,4, 

^84 

12*82 

24,56 

23.51 

25,28 

24,30 

26  .01 

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*6»7CC 

25,59 

27-45 

26,28 

26.97 

28*89 

19,62 

^8,35 

30»34 

29,04 

31.  of 

-9»7^ 

32.51 

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33«23 

31,81 

33,9,5 

32*6° 

34,6: 

3»»9 

35,40 

3,88 

36.  12 

4,58 

Uep. 

La\ 

46.1    Deg. 

a*«32P 


T  R  A  V  E  R  S  E    T  A  B  L  E.             8c 

3  C 

43   Deg. 

43*  Deg- 

43!  Deg. 

_434  Peg 

o  p 

•* 

La  . 

D.-P 

Lat. 

DCP. 

Lau_ 

Dep. 

L,a 

Dep 

r3  ' 

51 

37,30 

34,78 

37,i5 

34,94 

36,99 

35,n 

^36,84 

35,2 

5» 

52 

38.03 

35.46 

37,88 

35,63 

37,72 

35,79 

37,56 

35,<)6 

52 

5-° 

38,76 

36,15 

38,60 

36,31 

38,44 

36,48 

S  8,  29 

36,6.5 

53 

54 

39*49 

36,83 

39,33 

37,'>o 

39,  J  7 

37*17 

39.0' 

37,3- 

54 

40,22 

37,5i 

40,06 

37,69 

39,90 

37,^6 

39,73 

38,00 

55 

5<5 

40.96 

38.19 

4°,  79 

38,37 

4",62 

33,55 

4°>45 

38,7^ 

56 

57 

4Z,69 

38,87 

41,52 

39>o6 

41,33 

39,24 

41.17 

39*42 

57 

58 

42,42 

39,56 

42,25 

39,74 

4**°7 

39  92 

4  1,9* 

4°,l  1 

58 

59 

43>i5 

40,24 

42,97 

4:'.-43 

42,80- 

40,61 

42,62 

4.o,8< 

59 

•  60 

43  88140.92 

43,70 

41  11 

43,52 

41.30 

43  34 

4i,49 

^ 

61 

44,61 

41,60 

44  43 

41,8 

44,25 

41  99 

44,06 

42,1^ 

61 

62 

45,34 

42,28 

45,  16 

42,48 

44>97 

42:68 

44,79 

42,87 

62 

63 

46,08 

42,97 

45,89 

43,i7 

45,7* 

43,37 

45,  51 

43  57 

63 

64 

46,81 

43,65 

46,62 

43,85 

46,42 

44.05 

*6,»a 

44,2*. 

64 

47,54 

44,33 

47,34 

44,54 

47,15 

44,74 

46,9£ 

44,9c 

65 

66 

48,27 

45,0' 

48,07 

45,22 

47,87 

45543 

47,61 

45,64 

66 

67 

49,00 

45,69 

48^0 

45,9i 

48,62 

46,12 

48.41 

46,3; 

67 

68 

49*73 

46,38 

49,53 

46:59 

49,33 

46,81 

49,12 

47,02 

68 

69 

50,46 

47>°6 

5°,26 

47,28 

50,05 

47,5° 

49>8/| 

47,7i 

69 

70 

5*,i9 

47,74 

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47.96 

50.78 

48,18 

52,57 

48,41 

7:) 

71 

5i,93 

48,42 

5i,7i 

48,65 

5',5o 

48,87 

51,29 

49,  i* 

71 

72 

52,66 

49,10 

52,44 

49,33 

52,23 

49.56 

52,,  i 

49,79 

72 

73 

53-39 

49,79 

53,  17 

50,02 

52,95 

50,25 

52,7, 

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73 

74 

54,12 

5o,47 

53,9o 

50,70 

53,68 

50,94 

53>4^ 

5  J  ,  !  7 

74 

75 

54.8? 

51,15 

54,63 

51-39 

54,40 

51,63 

o4-i; 

i  i  >86 

75 

76 

55,58 

5X,83 

55,36 

52.07 

55,13 

52,31 

54,9c 

,52.55 

76 

77 

56,31 

52,5' 

56,08 

52,76 

55,85 

53,(:0 

55,62 

33,2 

77 

78 

57,°5 

53-20 

56,81 

53,44 

56,58 

53»69 

56.34 

53,94 

78 

79 

57,78 

53,88 

57,54 

54,i3 

57,31 

54,38 

57,0; 

54,6. 

79 

8 

5^51 

54*56 

58,27 

54,81 

58,03 

55  °7 

57-  7  v 

^.5.32 

81 

59*24 

55,24 

59>0t 

55^50 

58,76 

55,76 

5^,5! 

56,01 

?I 

82 

59,97 

55,9* 

59,73 

56,98 

59,48 

59,23 

56,7° 

82 

83 

60,70 

56,61 

60,45 

56,87 

6>,21 

57*'3 

59-9^ 

57,4( 

83 

84 

6',  43 

57,29 

61,18 

57356 

60,93 

60,68 

84 

85 

62,17 

57:97 

61,91 

58,24 

61,66 

58*51 

61,  40 

58,78 

85 

86 

62,90 

58,65 

62,64 

58,93 

62,3*5 

59.20 

62,12 

59,47 

86 

87 

63,63 

59-33 

63,37 

59,6i 

63,11 

59«89 

62,85 

60,16 

87 

88 

64,36 

60,02 

64.10 

60,30 

63,83 

60,58 

63,57 

60,85 

88 

89 

65.09 

6o-,7v, 

64,82 

60,98 

64,56 

61,26 

64,29 

89 

2- 

65,82 

61,38 

65,55 

61,67 

65.28 

61,95 

65,01 

^2,24 

9o 

91 

66,55 

62,06 

66,28 

62.35 

66,01 

62,64 

65,74 

b^,93 

yi 

92 

67,28 

62,74 

67,01 

63,04 

66,73 

63,33 

66,46 

63,62 

92 

93 

68,02 

63,43 

67,74 

63,72 

67.46 

61,02 

67,18 

64,3' 

93 

94 

68,75 

64,11 

68,47 

64,41 

68.19 

64,71 

67,9C 

65,00 

94 

95 

69,48 

64,79 

69,20 

65,09 

68,91 

65»39 

68,62 

65,6^ 

95 

96 

7°,2i 

65,47 

69,9* 

65,78 

69,64 

66,08 

69,35 

56,39 

96 

97 

70,94 

66,15 

70,65 

66,46 

70,36 

66,77 

70,07 

57,oi< 

97 

98 

71,67 

66,84 

67^5 

67,46 

70,79 

^7,7/ 

99 

72,40 

67.52 

72,11 

67,83 

7!'si 

68,15 

71,51 

8,46 

99 

loc 

73,M 

J8.20 

72.84 

68,52 

72,  H 

68,84 

72,24 

9,15 

oo 

>    SS 

Ucp. 

Lat. 

Dep. 

Lai. 

^at. 

Dtp. 

.at. 

3*" 

J  Q   47   Deg, 

46J  Deg. 

46i  Deg. 

461  Dc£. 

TRAVERSE     TABLE. 


&.UW 

1  °l 

44   Dc^. 

44i  De^.    ||    44  5-  Deg.  ||    44  3C  ^e^. 

45  "-Dp?. 

o  g 

f  *> 

L*. 

D?p. 

L*  .  , 

D-p  ||  L  : 

L)ep.  ||  Lat. 

Jep 

La- 

L>e*> 

33     ff 

1      1 

0,72 

0.69 

0,7. 

0,70 

0,71 

0,70  ||    o, 

071 

0,71 

0,71 

I         ^ 

2 

1,44 

i»89 

H3 

!>4 

1-43 

1,40 

1,42 

J,4l 

1,41 

1,41 

2 

Q 

2,10 

2,--)8 

8,15 

2,09 

2,14 

2    I  , 

2,13 

1,11 

2,12 

2,12 

3 

4 

2.88 

1,78 

O  _ 

2.79 

2,85 

2.80 

2,84 

2,83 

2,83 

4 

5 

3.60 

3,47 

3,5" 

3  49 

3,57 

3,5^ 

3,55 

3-52 

3-54 

3,54 

5 

6 

4*3* 

4,17 

4,30 

4,19 

4,28 

4,21 

4,26 

4-22 

6 

7 

5>°4 

4,86 

^,01 

4,88 

4*99 

4-91 

4,97 

4,93 

495 

4^9,7 

7 

8 

5,75 

5*56 

5-73 

558 

5,7i 

5-6i 

5,68 

5,63 

5-66 

5-66 

8 

9 

6,47 

6,25 

6.45 

6,28 

6,42 

6,39 

6,34 

6.36 

6,36 

9 

10 

7.19 

6,95 

7.16 

6,9* 

7-  *  3 

6  01 

7,io 

7,04 

7.07 

10 

1  1 

7,91 

7,6"4 

7,88 

7,68 

7.^5 

7  7i 

7,8i 

7,74 

7.78 

7,78 

11 

12 

8,63 

8,34 

8,60 

8,37 

8,56 

84! 

8,5<2 

8,45 

8.49 

8,49 

12 

13 

9>35 

9*°3 

9.31 

9'°7 

9)27 

9,11 

9>2a 

9.15 

9,*9 

9,19 

13 

10*07 

9,73 

10,03 

9,77 

9-99 

9,81 

9»94 

9,86 

9>9° 

9,90 

14 

15 

10,79 

10,42 

10,74 

10,47 

10,70 

10,51 

Xo965 

10,56 

to,6i 

10,61 

15 

16 

11,  5l 

H,li 

11,46 

ii,  16 

11,41 

11,21 

Ii,36 

11,26 

11,31 

11,31 

16 

12,23 

11,81 

12,18 

11,86 

12   13 

11,92 

!2.O7 

12,02 

12,02 

17 

18 

12,95 

12  5  > 

12,89 

2.56 

12,84 

12,62 

12,78 

12,67 

n,73 

12,73 

18 

J9 

13.67 

13,20 

i3,61 

13,26 

13,55 

13-32 

13-49 

13,38 

13,43 

I3?43 

19 

20 

i4,'i9 

13,89 

14.33 

13.96 

14,26 

14  02 

14,20 

14,08 

14,14 

2O 

1     21 

J4><59 

14,65 

14,9814,7* 

14,91 

H  78 

i4j85 

14,85 

11 

22 

15,83 

15,  2* 

15,76 

15,35 

15,6915.42 

i,562 

J5*49 

15,56 

15,56 

22 

23 

16,54 

15,9'^ 

16,47 

16,05 

10,4°  16.12 

16  3^ 

16,19 

16,26 

i6,2<5 

23 

24 

17,26 

16,67 

<6.75 

17,12  16,82 

I?-;  4 

1  6,9 

16,97 

16,97 

24 

25 

17,98 

*7?37 

17,91 

17,83 

17,52 

17,75 

17.60 

17,68 

17,68 

25 

26 

18,7 

18  06 

18,62 

18,14 

18,54 

l8,22 

48,40 

18,30 

18.38 

18.38 

26 

27 

19,42 

18,76 

19>34 

18.84 

19,26 

l8,92 

19^7 

19,01 

19,  >9 

27 

28 

20,14 

19,45 

20,06 

19  54 

19:97 

19,63 

19,89 

19.80 

19,80 

28 

2() 

20,86 

l  >15 

20,77 

20,24 

20,68 

2  ,33 

^    60 

2     .42 

20,51 

20,5 

29 

|      30 

•21,58 

2'>.84 

21,49 

20  93 

21,40 

2  1 

2:     1   '. 

21,2 

21    2 

30 

3l 

22,3,) 

21.53 

22,21 

21,63 

22,11 

21,73 

22.     - 

11,82 

21,92 

21,92 

31,     1 

32 

23,02 

22,23- 

22,92 

22,33 

22,82 

2i,7o 

22,53 

22,63 

22,63 

32  1 

33 

23,74 

22,92 

23,64 

23)54 

23,13 

13  44 

23,23 

j  23^33 

23,33 

33 

34 

24,46 

23,62 

24,35 

23,72 

24-  *5 

23,83 

24-     D 

23--94 

24,  ^4 

H,  '4 

34 

35 

25,^8 

24,3  l 

25,07 

24,42 

24,96 

14,53 

24,86 

24,7 

24>75 

35 

36 

25,00 

25,01 

25,79 

25.12 

25,68 

25,23 

15)57 

25,34 

25,4^ 

15-46 

36 

37 

26,62 

2,5,7f> 

26,  51 

25,82 

26,39 

25-93 

26,^8 

26  05 

126,16 

26,16 

37 

33 

27.33 

26,40 

27,22 

26,52 

27,10 

26,63 

26.99 

26,75 

26,8 

<2b,87 

38   1 

39 

18,05 

27,09 

27,94 

27,21 

27,82 

27,34 

27,7 

27.46 

27,58 

17,58 

39 

40 

28,77 

2"  ,70 

eS.6' 

27,9  « 

2R  ^ 

28.04 

28,4 

28.16 

28,28 

28,38 

40 

29,49 

28,4* 

29,37 

28,61 

29,24 

28,74 

29?i 

28,86 

18,99 

28,99 

42 

30.21 

29-!^ 

30,08 

29:31 

29.96 

29,44 

19,83 

29>57 

29,  7r 

29,70 

42 

43 

30,93129,87 

3  >«8c 

30,00 

3^,67 

30,14 

3-M4 

:  3'M 

3°»4i 

43 

44 

3  1>°5 

30.50 

31,59 

3O,7O 

31,38 

30.84 

3  1*25 

3  ^98 

31,1 

31,11 

44 

45 

32.37!3t,26 

32,23 

3'  '4° 

32,i-c 

3  ',.54 

31  9 

31,68 

31*8 

31,82 

45    | 

46 

33.0931,95 

32,9^ 

32,10 

3z,8i 

32,24 

31,6 

32,38 

3,2,5 

3Z>53 

46 

47 

33,8*31,05 

33,67 

32,80 

33-52 

32,94 

33'3 

33  °9 

33,  8£ 

33,13 

47 

48 

34  5333-34 

34,  38 

33»4.9 

34,24 

33,04 

34.  °S 

83»79 

33,94 

33^94 

48 

49 

35-2534»°4 

35-  IG 

34»r9 

3^95 

34,34 

34,5° 

34-6,- 

34,65 

49 

1  _5  o_ 

3^97j34-73 

35-K* 

34.80 

35,66 

35,^5 

35  »  5 

35,20 

35,  3f 

35-3^ 

J>° 

^r  ~ 

D-o.I^t.    11  Dep 

Lat. 

D^p. 

La',    jl  D 

L.a  .    |[  Uep.Lat. 

ejs    • 

S  6 

4  i*    Deg.  SI  453-    Dcg 

4si  Deg.  II    45^  Deg-  ||    45   Deg. 

Q  t 

*£fTfts5s                                                  s  iisgan 

TRAVERSE    TABLE. 


9t 


|! 

—  "—?•?•—  ••- 
441     Oeg. 

f"f%            Jp*       II  flr*                  ><•       II  *?*t  j              K» 

45    Deg. 

v,  r! 

i 

i 

L*r.  |Oe->.  (I  L,  . 

Jan.  ||  La.-. 

>  P- 

L           L)  -o 

?  3 

51 

6,69 

5  43 

36,5,-i 

5,59  ||  36,38 

35,75  11  36,22 

35}9" 

36,06 

6,06 

51 

7,4> 

6    12 

37,25 

6,29  ||  37,09 

36,45  (I  36,93 

36,61 

36,77 

6,77 

52 

53 

8,1  a 

6.82 

37,9° 

6,98  II 

37,80 

37,15 

37,64 

37j3i 

37,4> 

7,48 

53 

54 

8,84 

7,51 

38.68 

7.68 

38.52 

^7,8,5 

38,35 

38,02 

8,18 

54 

55 

9,56 

8,21 

39,4° 

3  ,38 

39,23 

38,55 

38,72 

38,89 

3889 

55 

56 

0,28 

0,90 

40,11 

:.9  .08 

39?94 

39,  a5 

39-77 

39,42 

39>6 

]Q  60 

56    j 

57 

l,oo 

9,6o 

40,83 

39,77 

40,66 

39>95 

40,48 

40.13 

4053' 

40.31 

57 

5^ 

1,7 

0,29 

4»,55 

40,47  j 

41,37 

40,65 

41,19 

40,83 

41,01 

.,1.01 

58 

50 

2,44 

0,98 

42,26 

42,08 

4X,35 

41,90 

1I»54 

41.72 

59 

6- 

3.16 

U68 

42.9S 

41.87! 

42,79 

4^,05  ! 

42.61 

42,24 

42?48 

42,43 

60 

61 

3-8 

2,37 

43,69 

42,57| 

4&51 

42,76 

43,  3* 

42,94 

43.13 

43  13 

61 

62 

4,60 

QjO7 

44,4' 

43,26 

44,22 

43*46 

44,   3 

43»65 

43-84 

43,84 

62 

63 

5,32 

3,76 

45,13 

43.96 

44,93 

44,16 

44,74 

44*35 

44,55 

44,55 

63 

64 

6,04 

4,46 

45.84 

44,66   I 

45,6,5 

44.86 

45-45 

45,06 

45,25 

64 

65 

676 

5>  *  5 

46,56 

45,36 

46,36 

46,16 

45.96 

65 

66 

7  48 

45-85 

47,28 

l6,°5  i 

47»°7 

46,26 

46,87 

46,46 

46,67 

^6,67 

66 

6-7 

48,2. 

47,99 

46,75 

47'79 

46,96 

47,58 

47,  17 

47.38 

47,38 

67 

68 

4892 

47,24 

48,7* 

47,45  £ 

48,50 

47,66 

48,29 

47,87 

48,oc 

48,08 

68 

69 

963 

4o  93 

49»42 

48.15 

48.36 

49,00 

48,58 

48,79 

48.79 

69 

£0 

o  35 

48.63 

5(),I4 

4«,?5 

49,93 

49,06 

49,28 

49.5 

4Q-.50 

70 

71 

51,07 

49,;^ 

50,86 

49-54  j| 

50,64 

49.76 

50,42 

49r98 

50,20 

50.20 

72 

5',79 

5,),  02 

5M7 

50,24  1 

5i,35 

50,47 

51,1- 

50,69 

5  ,9J 

50,9l 

72 

7S 

52,5 

50,7! 

5°,94 

52,07151,17 

51,84 

5^39 

51,62 

51,62 

73 

74 

53,23 

53,o 

52,78:51,87 

5*,55 

52,10 

52,33 

5»-33  74 

•75 

53,95 

52,10 

53,72 

52,33  || 

53-4952,57 

53)26 

52.80 

53>°3 

53,03  75 

76 

54,6 

c*  79 

54,44 

53^3 

54,21 

53,17 

53-97 

53»5i 

53,74 

53»74i  76 

77 
78 

79 

55>3 
56,1 

54-1* 
<4,88 

55,8 
56,59 

53,73  i 
54,43  1 

54,9253,97 
55,6354,67 
56,35!55,37 

54,68 

55>39 

56,10 

54  21 
54»9i 
55,62 

54,45 
55,15 
55,86 

54,45 
55,15 
55,86 

77 
78 
7Q    1 

57  •  5 

55  -5"1 

ill  3 

.5  5  82  | 

57.o6'56s  7 

56,8. 

56,32 

56,57 

56,57  80   | 

8 
82 

58,2 
58,9 

56,^7 
56,96 

58,02 
58,74 

5^52  j 
57,22 

57,77|56,77 
58,4957,47 

58^24 

57^73 

577S9B 

57,28 

81 
82 

83 

59-7 

59,45 

57,92 

58,18 

58,9,5 

,58,43 

58,69 

.58,69 

83 

1    84 

6  ,4 

58,35 

60,17 

58,61 

59,91 

58,88 

59,66 

59,1  4 

59,40 

59.4° 

84 

85 

61,1 

59,05 

60,89 

59,3:  1 

60,63 

59,58 

60,37 

59,84 

:  60,  I  ( 

63,10 

85 

86 

61,8 

59,74 

61,60 

60,  oi  1 

61,3460,28 

61,08 

60,55 

60,8 

60,81 

86 

8 

62,5 

60,44 

62,32 

60,71 

62,0560,98 

61.79 

61,25 

6.1,52 

61,52 

87 

8 

63,3 

61,13 

63,03 

61,41  j 

62.7^61.68 

62,  5c 

61.95 

62,  z[ 

62,23 

88 

89 

64,0 

61,82 

03,  7« 

62,10  1 

63,4862,38 

63,21 

6?.,  66 

62,9, 

89 

9 

64.7 

62,52 

64.47 

62,80  j 

64,10 

163.08 

63,92 

63.36 

63,64 

63,64 

22 

9 

65  4 

63,21 

65,1? 

63,5° 

63,78 

64,63 

64,07 

64,35 

64,35 

91 

9 

66.1 

63,91 

6,5,9c 

64,20 

6,5,6: 

6448 

65,34 

64,77 

65j(>, 

65.  '5 

92 

g 

66,q 

64.60 

66.62 

64,89 

66,3- 

65,18 

1  66,0. 

65,47 

65,76 

65-76  93    i 

9 

67,6 

6.5i3° 

67,  3c 

65,59  1 

67,0,5 

>  6.5,89 

66  7( 

66.18 

66,37 

66.47 

94 

i    9 

68,3 

65,99 

68,0^ 

66,29 

67.7< 

.66,59 

67,47 

66,88 

67,.b 

67,18 

95 

9 

69,0 

66,69 

68,7^ 

66,99  ! 

68,4- 

'67,29 

67,59 

67,88 

07,88 

96 

9 

69.7 

67,38 

69,4? 

67,69 

69,  H 

167,99 

68  8s 

68,29 

68,59 

58,59 

97 

-9 

7°-5 

68,08 

70,2C 

68,38  1 

69,9^ 

68,59     69,  6c 

68,99 

69j3' 

69  30 

98 

9 

71,2 

6877 

70,9] 

69,08 

7'  »,6i 

69,69     7o,3' 

69,7° 

70,0; 

70,00 

99 

i, 

71.9 

^9,47 

716? 

69,78  | 

7i,  3c 

70.09  II  71,0, 

70.40 

,70,71 

70.7' 

jOO 

I  <= 

D-p    Lai.    jj  Dep 

Lat.    | 

1  Do.  Lit.     II  D:tp.  Lat. 

Dep 

.at. 

«   4K 

j§  Q     46   Deg.  .  ||  45  T  Deg-    1 

45i  Deg-    II  45i  Deg- 

45  Deg. 

a  t 

I 


a  A 


£                     NOTE. 

1 

The  index  of  the  logarithm  of   e- 

very  integer  number  confifting  of  on- 

ly  one  figure  is  o,  of  two  figures  i, 

of  three  figures  2,  of  4  figures  3 

;be- 

ing  always  an 

unit  lefs  than  the 

num- 

ber  of  figures 

contained 

in  the 

inte- 

ger  number. 

In  this  table,  as  is  ge- 

nerally  the  cafe,  the  index  to  the  lo- 

garithnj  of  every  number  above  700  is 

omitted  ;yet  in  the  operation  muft  be 

prefixed  according  to  this  remark  ;  fo 

the  logarithm  of  700  is  2,84510,  and 

of  7000  is  3^84510,  and  fo  of  the 

reft. 

ATa 

)le  of  Logarithms  from  I  to  10,000. 

No. 

_Log. 

No 

Lo~£. 

No.|  Log.  jNo 

j^Qg.    |No.  ^  Log,   j 

j 

o.ooooc 

21 

I.32222~4l 

1.61278  61 

1.78533;  8  1 

1.90848 

2 

0.30103 

22 

3424      42 

62325 

62 

79239 

82 

91981 

3 

0.47712 

23 

36173 

4-3 

63347 

63 

79934 

83 

91908 

4j 

0.60206 

2^ 

3802 

4^ 

64345 

64 

80618 

84 

92428 

t; 

0.69897 

25 

39794 

41 

65321 

65 

81291 

85 

92942 

6 

0.77815 

26 

4149^ 

46 

66276 

66 

81954 

86 

93450 

7 

0.84510 

27 

43136 

47 

67210 

6? 

82607 

87 

93953 

8 

0.90301} 

28 

447i6 

48 

68124 

63 

83251 

o  r> 

oo 

94448 

9 

0.95424 

~9 

46240 

49 

69020 

69 

83885 

89 

94939 

JO 

l.OOOOo 

i° 

47712 

69897 

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00 

95424 

ii 

1^04139 

3* 

1.49136 

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1  -70757 

71 

1.85-726 

91 

1.95904 

12 

07938 

5^515 

52 

71600 

72 

85733 

92 

9^379! 

J3 

11394 

1 

51851 

53 

72428 

73 

86332 

93 

96848 

J4 

14613 

53*48 

54 

73230 

74 

86923 

94 

9?3T3 

ID 

17607 

35 

54407 

55 

74036 

75 

87506 

95 

97772 

36 

20412 

55630 

56 

74819 

76 

S8o8i 

96 

98227 

17 

23045 

37 

56820 

57 

75587 

77 

88649 

97 

98677 

18 

25527 

57976 

58 

76343 

78 

89209 

9« 

99123 

;     JO       -^7^*75 

3  20}  30103 

39 

40 

59*08 
60206 

59 
60 

77085 
77815 

I9 
80 

89763 
90309 

99 
100 

99564^ 

2.000CC^J 
IWt*?»fcJ  -t'^T 

Logarithms  from 


i  to  10,000 


^G^M-RtB 

"3No.|  o 

i 

3 

3  |  4    51.6    7 

r--1"^ 
0034? 

C077r 
01J.;, 
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02445, 
0285> 

0326? 
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0406,' 

0484. 
05231 
05614 

05994 
06371 
06744 
07114 
074.82 
07846 
53207 
08565 

10633 
10992 
H327 

1  1  66? 
11991 

123-20 
12646 
12969 
13290 
13609 

*3925 
14239 

14860 
15168 

-5473 
15776 
16077 
16376 

172001 
17551 

soiMjj 

|oo8i7  \\ 
01242 
OI66I 
02077 
02490 
02893 
03302 
P37°3 

5o4493 

04883 

05269 

05652 
'06032 
106408 
' 
07151 
075IS 
07882 

?100 
;  ICI 
102 
103 
IO4 
105 

106 
107 
108 
109 

coooo 
00432 
00860 
01284 
01703 
02119 

02531 
02938 

03342 
03743 
0413, 
04532 
04922 
05308 
05690 
06070 
06446 
06819 
07188 
07555 

00043 

30475 
00903 
01321' 
01745 

02l6v/. 

02575 
02977 
03383 

037jh 

^0087 
005  1  F 
00945 
31368 
31787 
0220?. 
026l2 
0301$ 

03822 

001  70 
00561 
00988 

014  10 
01828 
02243 
02653 

03060 

03463 

07802 

00173 
00604 
01030 
01452 
01870 
02284 
02694 
03100 
03503 

01072 
01494 
01912 

02325 

-2735 
03141 

03543 

04727 
05"5 

05500 
05880 
06258 
06633 

07004 
07372 

07737 

00261: 
00689 
01115 

01536 
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02366 
0277.' 
03181 
03583 

04766 
05154 
05538 
05918 
06296 
06670 
07041 
07408 
0777-; 

00303 

00732 
01157 
01578 

02407 
02816 
03222 
03623 
04021 

04415 
04805 
05192 

05576 
05956 

o6333 

06707 
07078 

07445 
07800 

no 
in 

112 

"3 
114 

"I 

116 
117 
118 
£19 

120 
121 
122 

124 
125 
126 

127 

129 
I30 

133 

134 

J36 
138 

04179 

04571 
04961 

05346 
05729 
06108 
06483 
06856 
07225 
07591 

04610 
04999 
^5385 
05767 
06145 
06521 
06393 
07262 
07628 

34257 
04649 
05038 
05423 
05805 
06183 

06558 

06930 

07298 

07664 

04297 
04688 

05077 
05461 

05843 

06221 

06595 
06967 

07335 

07700 

07,918 
08279 
08636 
0899! 
09342 
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10037 
10380 
10721 
11059 

07954 
08314 
08672 
09026 
09377 
09726 
10071 
10414 

I0755 
11093 

07990 
08350 
08707 
09061 
09412 
09760 
IOI06 
1044.9 

!°?*§ 

08027 

08386 

08743 

09096 

09447 
09795 

10140 

10483 

10823 
11160 

11494 
11826 

12156 

12483 
12808 

13767 

14082 

0003 
08422 
08778 
09131 
09482 
09830 
10175 

10517 
10856 

01  93 

0809-; 
08458 
08814 
09167 

09517 
09864 
10209 
^551 
10890 
11227 

0^135 
08497 
08849 
09202 
09552 
09890 
10243 
10585 
10924 
11260 

08171 
o  529 
08584 

09587 

°9933 
10278 
10619 
10958 
1  1  204 

FToiO7 

11959 
12287 
12613 
12937 
13258 
13577 
13893 
14208 

14520; 
£43>9j 

15442 
15746 
16047 

17231 

17522 

[08243 
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10003 
10346 
10687  j 
11025 
1  1361 
11694 
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C2'j  12 
12678 

13640 
^956 

145*2 
14891 
15198 
15503 

t;,8o6 

16997 
17580 

^394 
11727 
12057 

12710 

13°33 
13354 

13672 

i3988 

14301 

11428 
11760 

12090 
12418 
12743 
13065 
13386 
13704 
14019 
11333 
14644 

*4953 
15259 
15564 
15866 
16167 
16465 
16761 
17°55 
7  34  8 

11461 

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12123 

12450 

I2775 
13098 
13418 

13735 
14051 

14364 

ii  060 
12189 
12516 
12840 
13,62 
13481 

14114 
14426 

11561 
11893 

12222 
12548 
12S72 

13513 
13S30 

1445? 

"594 
11926 
12254 
12581 

12904 
13226 

!3545 
13862 
14176 
14488 

147^8 
15106 
15412 

15715 

16017 

17202 
1  7  4-9  3 

140 
141 
142 

144 

145 
146 
147 
148 
149 

152 

154 
155 
156 

Ki  I5l 

fcx5» 

-J159 

~T.C':& 

14613 
14922 
15229 
15534 
15836 
16137 
16435 
16732 
17026 

17319 

14075 

i4983 

15290 

15594 
15896 
16197 

16495 
16791 
17085 

^7377 

14700 
15014 

I5927 

16227 
16524 
16820 
17114 
17406 

14737 
15045 

15351 

15957 
16256 

16554 
16850 

14768 
15076 
15381 
15685! 

J5987J 

1658., 

16879! 

174641 

17609 
17898 
18184 
18469 
18752 

I9°33 
19312 

19590 
19866 
20140 

17638 
17926 
18213 
18497 
18780 
19061 
19340 
19618 

20167 

17667 

'7955 
18241 

18526 
18808 
19089 
19368 

19645 
19921 

20194 

17696 

|.  :</"-', 
18270 
18554 
18837 
19117 
19396 
19673 
19948 

20  2.  :2 

1772517754 
18013  18041 
18298118327 
18583^8611 
18865118893 

19145  '9[73 
19424  19451 
19700(19728 

19075-20003 

17702 
18070 

1.8355 
18639 
18921 
19201 

19479 

19756' 
20030 

1  7  jji  i:  1  7  840  1  7  869 

iHo  .I';  '18127!  I  8156 
18384.18412'!  8441 
186671869618724 

i8949;i8977'i9oo5 

19229  i9257;i92S5  i 
1  9507  19535,  19562  | 

^0058  7.0085  2OI  12^ 

1682253122557 


i6oh2789h3,8i4 


12583 

22840 


171 


174 


23045,23070 
2330023325 

553;?'3578 


24055:24080 


2430424329 
176245512457' 

2479724822 
17825042125066 


23090 
-3350 


22350  22375122401122427  22453 

226o3  22634  2266o!22686'227  I  r 
2286622891  22917122943  22o68 


23121 
23376 
23628 
23880 
24130 

24353*4378 

2460^24625 
24846(24871 
25091 


234CI 
23654 
23905 


i2£E52?sl*53JLS  2  53  345253  5 8  25382 
1 80  25527,25551 25575(25600  25624 


527125551 
2576825792 
26007  26031 
26245  26269 


2671726741 


26951  26975,26998:27021 
271842720-;   723127254 
746227485 
7692127715 


27646 


27^75 


18.-; 
186 
187 
188 
189 
190 


19328556 
194 

195 

196 

T9 
198 

I  or 


25575125 
25816125840 
26055:2607^ 
16292(36316 


26505  26529.26552 


26764126787 


28126 


28803 


29003 


29666 


90 

92 

29469 


29-385 


200  30103 
201 


.  99°7 


30535 
30750 


r43 
2053 


207 

2C8 


21332833 

2143304 


31806 

32015 

32222 


30982 


31408 

3161 

3182- 


3244' 

3265, 


33062 


332443326. 

3344.r  33/J/ 
33*4' 


22737 
^2994 


231722319812322323249 

234262345223477.3502 


442824452 
467424699 
4920  2494-" 


^139 


25864 
26102 
26340 
26576 


7921.27944 
814928171 


8601 
882528847 


9048 


29070 


927029292 

9491 

971029732 

992020051 


7967 

8194 

842 

28646 

2887. 

29092 

93i 

29535 

2975 

1997 


3081. 

31006 
31218312 
3*429_ 
316303166 


50146  30168 

3038413040 
7830600  3062 


3184831869  3189 

3209 


32284 


33=8 


33284 

33485:3350 


3oi33 
3x04 
3126 


3168 


3-3° 


367923704 
393023955 


9124204  24229 

P!')/1/1  X^  ~>  1  /l>?1 


516425188  25212 


6600 


5406 

564825672 
5888259^2 
612626150 
636426387 


2398 


24477 


24969 


25455 
156  )t 

25935 

26174 
26411 


26623  26647 


683.12685826881 

7068)27091  27114 


$8127091 
273°°27323 
27531 p7 554 

2776127784 


2757 
27807 


2798928012 


28443 
28668 
28892 
79115  . 
29336 2935^ 


28466 
28690 
2891, 


1955 
977 


Q 
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30230 
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3109 


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24254 

24502 

24748 

24993 

2523 

2547 

2572 

595 
2619 

6434 
2667. 
2690 
2713 


2760 

2783 

805 

2828 

285I 


28035 
2826 


28937 
291592918 
20380 
29601 

29820 2 


962 


2Q994j3ooi6  3033813005 

30211 

30427 

30642 

30856 

31069 

31281 


3047 1 '13049 

30685)3070 

30899 

3111213113 

3i323i3 


3170231723 

31911 

321 1 8(32139 


3232532346 
3*552 


32715327363275632 


3312233143 
33325'33345 


33224 
33425 
33626 

33766  33786  33806  33826 

3'3885133905|33925,33945i33o65  3398534005  34025,^ 
2if  34044:340 641 340 8^34 1 04-341 24 34i43!34i 63  34183  34203  34222', 


32960 


3J744,3: 


2l6o!l2l8 


32367:3238 


32572:3259 


32980,3300 

;5332' 


1985 

2246 
2505 
2763 
3019 
3274 
3528 

3779 
4030 
4279 
4527 
4773 
5018 
5261 
5503 


5744 

5983 
6221 

6458 

6694 

*928 

27161 

27393 
27623 
27852 
28081 
28307 

28533 
28758 
28981 
29203 
29425 
29645 
29863 
30081 


30298 

305i4 
30728 
30942 

3"  54 
31366 

3*576 
31785 
31994 

322-01 
32408 
32613 
32818 


Logarithms  from  i  to  10,000 


3459 
3479 
3498 


JTJ-*  JTJ"*-  O'rj't^  J*v.}ww  OT-,}UI- 

221  34439  34459;34478  34498  345iS  34537  34-557  34577 

222  34635  34655  34674  34694 347i3!34733  34752:34772 

223  34830  34850  34869  34889  34908.34928  34947(34/>7 
22435025  35044  35064  35083  3510235122  35141135160 

225  35218  35237  35257  35176  35295  35315  3533435353  3537 
I:6.  35S5 5J3°  35f>9  35468  3548835507  355^35545|3556 
35679135698  35717!35736J3575 
35870:35889  35908  35927J3594 


,  35983l36oo2 
?3?3SS3f^ 


231 

232 


f      lr ,      i\j^3"^ 
^36/363675436773 

-34369223694036959 

*31  37107  3712^  \11AA 


______  _ 

282  34301  34321  34341  3436034380  3440 

- 


3602] 


36567 


37475 


« 
37328 

37493  375" 


3762 

37731  37749l37767  37785:3780 
.     37894  379_i2  3_793jj37p4_9  3,7967 

240  3ao2i  38039  38057  38075  38093  381"  3813038148."  3816 

241  38202  38220  38238  38256  38274  38292  38310  38328  38346 
3^3«i  3«399  38417  38435  38453  38471  38439  38507(38525 

243  38561  38578  38596  38614  386,2  38650  3866838685  38703 
244.  3-8739  3  8757  3877538/923881038828388463886338881 
245  3"P*7  3«934  38952  38970  38987  39005  39023  39040  39058 
2.46  39093  39"i  39129  39146  3916439182  3919939217  39234 

3932o  3934°  39357  39375  3939  •:  394io 
3  3948o  394.98  3951  5  39533  3955r  39568  39585 

249  39020  39_637  39655  39672  39690  397073972439742  39759 

250  39794  398"  39829  39M  39863  39881  39895(3"^  - 


362I03622 

36399 
36586^      y 

36791 
36977 

37346 

3753C 


30059  30£7«  3^£97  3^1£2'3-2I1_ 
^ — y  36248,36267  36286  36305  3632 

36418  36436|36455!36474|36493  3651 
36605  36624 h6642;3666i|?668o  36698 
-  3681036829136847136866  36884 


JJ-  J-  JJ~  I-  jj--y  jjy ^ 

36040  36059  36078.36097 


36996  370i4;37033|3705i 


37365  37383'374oi  37420 
3754»  37566(37585  37603 


251  3996739985  40002  40019  40036  4005440071  40088  4010 

252401404015740174401924020940226402434026040278 

2534031240329403464036340381403981404154043240449 

254404834050040518405354055240569405864060340620 

256406544067140688407054072240739407564077340790 

25640*52440841  40858408754089240909409264094340959 

25740993  41010  41027  4104441061  410784-109541111141128 

258  41162  41  179  41  196  4i2I2  41229  41246  4126  3'4i28o'4i2  06 

259  41  3jjo  41347  41363  41380  4_i397  4I4I4  4i43oRi447  41464 
26041497415144153    4i5474i5644i58i4i5974i6T54l63T 
261  4166441681  41697  417144173141747417644178041797 

41830  4184    41861880186    11 


2634199642012420294204542062420784209442111  4212 
26442160421774219342210422264224342259422754229 

1  5«  42341  42357  42374  4239°  434°6  42423  42439  42455 

2488  42504  42521  42537  42553  42570  4258614260?  4.61  9 

42651  42667  42684427004271642732142749142765  4278 
268  428134283042846  428624287842894k29??|l292742943 
2694297  429i  43207J43024  4304043056143072143088  43104 

4p?te^^oife 


37383'374oi  37420  3743 


34420' 
34616 

35005 

35199 

3,392 

335 

35774 

35965 

3^ 

3634" 

3653° 
36717 

36903 
37088 

37456 

37639 

37822 
37985  3_8oo3 


41913419294194*41962 


2744377543791 
2754393343949439651439814399644612 


276  4409 1  441 07  441 22  441 3 8  441 54  ^169  441851442 
III  ^.t  tf:^  44^79 44205 443"  44326  44^4^3 


278  44404 44420  44436J4 1451  44467  44482 


4402844044  44059 


44217 


,443584437344389 

~oo2k 


38364 
38543 
38721 
38099 
39076 
39252 
39428 
39602 

9777 


40123 
40295 
40466 
40637 
40807 
40976 
4H45 
41313 
4146441481 


41813 
11979 

+2144 
42308 

42472 
42635 

-797 
^959 

43281 
43441 
43600 


1-075 
1-4232 


frcm  i  to  10,000. 


_,          .5.J. 

44716  4473  !-H  747144762  44/7<*!447  yd 


i28i4487i4488     .., 

282  4502545040  450564507  r45ob'6|45 102 


—    T  ^  */,'*/        f         i*/J~*i*Jl-.^J "  I   »  »/ 

2  83  4517  9  45*9445209  45225  45240  45" 


28^45637 


288.459394595445565,4*5 


2y: 


46380 
46538 


4^.835 


4.7129 
4-72764' 


25847422 


-1^55454556 


45652  45667145682145697 

yicfino  v--»TS/ii-8^t;f4^84  - 
5844600 


4580345818458 


4613 


4 6  25;  402 70  46 


46404:4641  r 


5684^58; 

4670214671'.  4673  ; 
4684^468644687 


1714.'  4715 s 


f643z 


46997  47012  4702''  47041 


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7305 -1-73H  47334  4-7: 


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47640 


29  9  !£7J>6 7 147 582 '47  5^6 ,47 6 1 1  47625 

'30047712  47727  47741  47755  4777C 
301 47857i47871 ,47885  47900.479i4  47929 
30248001  4801 548029 48044148058  48072 
303  48144.481 594817348 1 87  48202 
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40845423 


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4615046165 
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461804.61954623 
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46479  4649414650? 


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47040  47  "54  47009  ^7083 
47784  47799'478i3J47828 


3044828748302483164833048344 
"o5'48430 48444:48458 4847348487  4850 


48216 


3o6i48572'48586!4.86co486i  ^48629  48643  48657  4 
307'487i4'48728|48742 48756148770  48784 4879914 
3c8'48855t4886948883l48897|489i i  48929  4804^ 
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31449693 


315^9831 

51^49969 


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50106 


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949982 19996 


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5I  1'49276  4929049304493l£N9332 

3 1 2J4941 5  49429  49443  494 57 14947 1 
3i349554  495684958- 


49206 


49596I496 10 


9859 


4934649360 
49485  4949J 


49624 


49^3449748497 

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50010  50024 
50147  50161 


50i74 

50243,50256  50270  50284(50297  50311 
[79)55393!504£6  50420150433  5^447 


49900 


506  50'  5 


29:50547  50556  50569750583  50596 
50732 
50866 
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3  v,^/ —,507991508135085650839  50853 

323  5092o150934'5°947  50961  5°9745°987 
°-  51095  51108151121 


^809 
44963 
45117 
45271 


448244484- 

4497944994 
4513345148 
4528645301 

4543945454 


45728 
45875 


4.6627 

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4560.1 


4574345758 
4589445909 

4604546060 


6642)46 


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47°* 5 47ibo 


47232 


4737S|47392 
47538 
4768- 


4765447669 


47246 


4794347957 
4808748101 
4.823048244 

48373:48387 
4851548529 

--57|4867i 


48116 
482,59 
48401 
48544 
48685 


44855 
45009 


45469 
45621 

H5773 
45924 

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46225 

46374 
46523 
46672 
46820 
4-6967 
47114 
47261 
47407 

47553 
47698 

4784* 
47986 
48130 

^273 
48416 

45558 

48700 


148813  48827  48841 
4895/48968  4-898* 


4922 


49*38  ..  .     9 
49776  49790!498o3 

49927(49941 
5oo65|5co7 

501885020250215 

50325  - 
50461 


•i  325  51188  51202  51215  51228  51242^1255  51268  5128251295 
>j  326  51322^51335  5^48  51362  5i37§  5i388  5M02  514*5  5M28 


3275I4555I46«  51481  5149551508  51521 

il653 


51917 

52048 


.,  -  .  ,,516011516145162751640 
32_9,-112l2  "733  51746  5i759!ll7.72 
330(51851 


..  ,     -    -      -.  .,      '22-52035 

332:52114521271521405215352166 
333  52244  5  22  5752270' 57283152297 
_  '852401152414152427 
335  52504  52517  52530  52543!i  2556 


336526^452 


o52i<73152686 


51667 
5^7°5- 


52061 


7952192 
52323 
52453 
52581 
5269852711 


-^  337  52763  52776  52789  5280252PI4  52827152840 
y*,338 52892  5290452917  5293052943152956:52969 
JU839  53020  53033  53046  5 

#c» 


53°7-!!53o84!53c9753i10 


108  49122 
149262 


495i3|49527; 


0474:50488 


5074550759 
5088050893 


5H485II62 


5I5345I548 


51561 


5168051693 


51943 


51-56 


52074  52088 
52218 

5233("l52:49 
52466152478 


5-2400  52470  5^91 
52595152608  52621  || 

c"s*"ro/iico*7^'h7tcr'7*Tc:O  ' ' 


49679 
49817 
49955 
50092 
50229 
50365 
50501 


50637 
50772 

50907 
51041 

5*175 
51308 

5J574 
51706 

ilisj 

5f97° 
52101 


52491 


52724552737 


52852 
52981 


52866 
52994 
3122 


52750 


53135 


Logarithms  from  I  to  io,oao 


*No. 


341 


344 
345 
346 
3*7 
34<* 
34? 
35C 

351 

35: 

354 

355 
356 
35^ 


363 
364 
36 


(  3 


3275:53288 


533°i 


365653668 

378253794 
390853920 


563° 

575i 

5871 

5991 

56110 

5622 

5634* 

56467 

5658. 

567° 

5682 

5693 
57°5 
57*7 
5728 

5740 
575i 
5763 

5774 
5786 


1-368: 

53807 


54307 


*J  J  \+r»Jf  •*  >~>  s  V*  *J 

4033)54045  54058 
4158)54179 
1182154205 

4407] 

4F 
4654 

4777 
4900 

5023 
5145 

5267 


4419 

543! 
466- 
4790 
49 1 3 
5035 
5157 
5279 
5400 


5763 
5883 
6001 
,6122 
56241 
5636' 
5647* 
5659" 
56714 


5683 

5694 
5706 
57i8 
5729 
574i 
5753 
5764 
5776 

5787 


38057978(5799 
381  580925810 


38258206 
383583*° 


5821 
5833 


4444 
4568 


4802 
4925 
5°47 
5165 

5291 
5413 
5534 


5775 
5895 
601 

6.34 
625 

:637 

i649 

;66o 
5-672 


56844 
5696 

57*9 
5731 
742 
5754 
5765 
5777 
5788 


580 
581 
582 
583^ 


384' 58433  5844  584 
385585465855715851 
3865865958670586 
3875877158782587, 
388  58883  5889415891 
38';  58995  590061590 


«6$3X99[532" 

31453326  333 

44153453 
5675358o 


195 


69453706 
82053832 

945  53958 

^070  54083 


54208 


•32054332 


37  J  9 
3845 
397° 
4095 

4220 
4345 


704 


494< 


685 
697 
708 
,720 
i732 
i743 
J755 
5766 
5778 


5801 

581 

582 

5835 
5846 
858 
5869 
5880 
5891 
59°2 


390J59io6  59118  59129  5914 
391  59218  59229  59240  5925 


392* 
393' 


59329  5934°  59351  593 


59439594505946 


5947 


5o3 
615 
627 
639 


686 


721 

;73'3 
1 744 
J75^ 
576! 

'77 

;79 


4592 

47 1< 
483c 
4962 

So8^ 


593 
605 

617 
628 

(640 


S687 


57" 

5722 

5734 

5746 

5757 

576 

578 

570 


352533< 
479J534,- 
i6o5J536i8 

;73* 
;85' 
198. 


$25053263' 
533775339° 


53504 


53744 


53517 


54I 
5424 


5363* 53643 
5375753769 
53895 

|54o2o 
|54i33  54145 
[54258  54270 

54642 


54765 
54888 


3571543 
4481  544 
4605546 
47285474o|54753 
4851  5486 

49745498  .-  ,-  ... 
509655io8j55I2i|55i33 

52185523 
53405535 
546i  55473 
5582  555.94 


5524 
5536 


55255 

•  ^-^-  •  55376 
5548555497 


55606 


55618 


57°3  557I555727  55739 
5584755859 
55°55 P5907  55979 
215607456086  56098 

6182)56194156205156217 
630! 


563^6324;  5-6^6 
5643156443J56455 
565495^56156573 


("vja 

>6?73 


56667 
56785 


5667 
56797 


.168905690256914 
57008 570i# 57°3J 


56691 
56808 


57043 


7124  57136  57J48  57159 
5725257264157275 


3/*3*l* '  o  •"  ' 

57368  5738°  57391 
574845749^57507 


57357 
57473 
57588 

577°3 
57818 

5703^7044157955 


576oo576n 
57841 


57623 
57738 
578p 

57967 


5802- 
5813! 


58591 


5926 
5937 
5948 


595725958  59594 596of 


i 


3955966059671 

396  59769  59780  5979I>598°2|598 

397  59879  5989059901:59912  5992 

>399  60097  6oio8l6oii9  60130  6014 


./O    «  7 

58263 
58376 
58490 
58602 
5871* 
58827 
58939 
59051 


58388158399158410158422 
58501585125852358535 


59162 
59273 


_  .  58081 

58161  581722818458195 


5828658297 


58308 


*/   J  ~  ~\  J  w  J  *  —I*'   <J   *?\J   J*)J 

58614586255863658647 
58737 K8749  58760 
-      .   ,58850  588.61  58872 
58950(58961158973  58984 
59OQ5 


590625907359^84 


59I7359l84  59195  59-°7 
59284592955930659317 


5949^ 
5960^ 
04  59715  59726159737159748159758 


5993459945  5095f>|59900|59977 
60043  6oo54'6oo65|6oo7  5|6oo86« 
'0195* 


Logarithms  from  i  to  10,000 


r^No: 

?4oo 
401 

402 

4°3 

404 

405 
06 
107 
,08 
409 
4ic 
411 
412 
413 
4i4 
415 
416 
417 
418 
419 

o 

S0206 

5o3i4 
50423 
50530 
5o638 
50746 
30853 

^0959 

'uo66 

5lI72 

$1278 
5i384 
61490 

$1595 
61700 
61805 
61909 
62014 
62118 

6222T 

i 

n 

3)4    5  '  6 

7,8, 

Q  a 

0217 
0325 

°433 
0541 
0649 
0756 
0863 
o-7c 

1077 

1183 

60228 
60336 
60444 
60552 
60660 
60767 
60874 
60981 
61087 
61194 

6o239| 
60347 
60455 
60563 
60670 
60778 
60885 
60991 
61098 
61204 

60249 
0358 
0466 

°574; 

60681! 
60788 
60895 
61002 
1109 
61215 

60260, 
60369 
60477: 
60584' 
50692 
60799 
60906 
61013 
61119 
61225 

60271 
60379 
60487 
60595 
60703 
60810 
60917 
61023 
61130 
61236 

60282 
60390 
60498 
60606 
60713 
60820 
60927 
61034 
61140 
61247 

60293 
60401 
60509 
60617 
60724 
60831 
60938 
6l045 
6lI51 
61257 

°3C4$- 
0412 
0520 
0627 
60735 
60842 
60949 
^1055 
61162 
61268 

1289 
1395 

I5OC 

1605 

1710 

1815 

1920 

2024 

2128 

2232 

~2335 
62438 
2-541 
62644 
62747 
62849 
62951 

63053 
63154 
63256 

61300 
61405 
61511 
6l6l6 
6I72I 
61826 
61930 
62034 
62138 
62242 

£*3*5 
61416 

61521 
61626 
6i73i 
6i836 
61941 
62045 
62149 
62252 

6x321; 
^1426, 

<*Pl 

61637 

61742 
61847 
61951 
62055 

62159 
02263 
62366 
62469 
62572 
62675 
62777 
62880 
62982 
63083 
63185 
63286 

6133* 
01437 
61542 
61648 
61752 
61857 
61961 
62066 
62169 
62273 

61342 

61447 

6i553 
61658 
61763 
61868 
61972 
62076 
62180 
62283 

61352 
66$* 

61660 

6*773 

61878 
6l982 
62086 
62190 
62294 

6I363 
61469 
6l574 
6l6p 
61784 
6l888 
61993 
62097 
6^201 
62304 

61374 
61479 
61584 
61689 
61794 
61899 
62003 
62107 
62211 
62315 

420 
421 
422 
423 
424 
425 
426 
427 
428 
420 

2325 
2428 

2531 
2634 

2737 
2839 
2941 

3°43 
3144 
3246 

v.-i346 
62449 
62552 
62655 

62757 
62859 
62961 
63063 
63165 
63266 

'-356 
62459 
62562 
62665 
62767 
62869 
62971 

63073 
63175 
63276 

62377 
62480 
62583 
62685 
62788 
62890 
62992 
63094 
63!95 
63296 

63397 
63498 
63599 
63699 
63799 
63899 
63998 
64098 
64197 
04296 

62387 
62490 

62593 
62696 
62798 

62900 
63002 
63104 
63205 
63306 

62397 
625OO 
6260-3 
62706 
62808 
62910 
63012 
63II4 
63215 
63316 
63417 
63558 

636l9 
63719 
63819 
63919 
64018 
64Il8 
64217 
64316 

62408 
625II 
62613 
627l6 
628l8 
62921 
63022 

63I24 
63225 

63327 

62418 
62521 
62624 
62726 
62829 
62931 

63033 
63134 
63236 

63337 

43° 
431 
432 
433 
434 
435 
436 
437 
438 
£31 

44° 
441 
442 

443 
444 

445 
!  446 

44-7 
448 

440 

63347 
63448 

<$3548 
63649 
63749 
63849 
63949 
64048 
6414- 
6424^ 

63357 
63458 

23558 
63659 
63759 
63859 
63959 
64058 

6415" 
64256 

63367 
63468 
63568 
63669 

63769 
63869 
63969 
64068 
64167 
64266 

63377 
63478 

63578 
636/9 

63779 
63879 
63978 
64078 
64177 
64276 

63387 
65488 

63589 
63689 
63789 
63B89 
63988 
64088 
64187 
64286 

63407 
63508 
65609 

63709 
63809 

6400? 
64108 
64.207 
64306 
64404 

64503 
64601 
64699 

64797 
64894 
64992 
65089 
65186 
65283 

63428 
63528 
63629 
63729 
65829 
63929 
64028 

&1 

64325 

63438 
63538 
63039 

63739 
63839 
63939 
64038 
64137 
64237 
64335 

64345 
64444 

64542 
64640 
64738 
64836 
6493.5 
0503 
65128 
6522 

64355 
64454 
64552 
64650 
64748 
64846 

64943 
6504^ 

65137 

65234 

64365 

64464 
64562 
64660 

647  5  F 
6485,6 

64953 
6505- 
65147 

65244 

64375 
64473 

64572 
64670 
64768 
64865 
64963 
65060 
65157 
65254 
65350 
(ir^jf 

65543 
6563 
657  34 
65830 

65925 
66o2c 
66115 
662  ic 

64385 
64483 
64581 
64680 

64777 
64875 
64972 
65070 
65167 
6526-, 

64395 
64493 
64591 
64689 
64787 
64885 
64982 
65079 
65176 
65273 

64414 

64513 
646ll 
64709 
64807 
64904 
65OO2 
65099 
65196 
65292 

64424 

64523 
64621 
64719 
64816 
64914 
65011 
65108 
65205 
65302 

64434 

64532 
64631 
64728 
64826 
64924 
65021 
65118 

65215 

65312 
65408 
65504 
65600 
65696 

65792 
65887 
65982 
66077 
66172^ 
66266C 

.;  45c 
45i 
45= 
45V 
45^ 
45 
.  45 

;  45 

&45 
*J45 

rr* 

°532 
6541 
65514 
6561 
6570 
6580 
6580 

^599 

6608 
6618 

6533J 
65427 
65523 
656  r<, 

65715 
-65811 

<F°f 
0000:1 

6609? 
66191 

65340 
65437 
65533 
65629 
6572j 
65820 

659*5 
6601 
6610 
66ioc 

65360 
65456 
65552 
65648 
65744 
65839 
6593: 
66030 
66124 
66219 

J53JO 
65466 
65^62 
656-58 

65753 
65849 

165044 
|66o3r 
66134 

166229 

65379 
65475 
65571 
65667 

65761 
65858 

65954 
66o4f 

6614- 
6623! 

65389 
65485 
65581 

65677 
65772 
65868 
65060 
66058 
66153 
66247 

65398 
65495 
65591 
65686 
65782 
65877 
65973 
66068 
66162 
66257 

Logarithms  from  i  to  10,000 

y&f******* 


•460  66276166285  <5o*2~r; 


41 


66374663796638; 


314 
66304166313 


66398 


]',  4 ''2  66464  66474  6648  3  . 

JH  463  66558  66567  66577  6  >58 

46466  5266661 6667o 6658 

465  66745  66755  667646677 

466  66839  6  584-8  66«  —  *  <  ^ 

467  6693  i  66  ;4i  66 

468  67025  6703467043' 

''  6  'H7  6712667136 

470  67210  I 


427 


'640: 

'6502 

.6596 

66689 

66-783  66-792166801  . 

66876  66885  66894  66904 


473 
474 
475 


478 


482 


48-8 


7578 


673^167320 
367413 

•-,  67504 

758767596 


76696767867688 


7761 


57770167779 
6786167870 


794367952:6796 


58395 
'8484 
8574 

8664 

'3753 
18842 
58$3J 

:1,906902C 

6910 

49 


67697l677o 
67-7886-7-7996 


6797o 
'43168052  68061 


8124 

82i4|68223j( 

830568314168323 


6840416841 

6849368502 

53583168592 


68673 

68762 
68851 
68940 


69117 


68771 


760 


5637866987 

07071 67080 
671546716467173 


5643' 
^653° 


56635  66614  56624  56633 
$569966708  <*«-  <*»- >« 


5  68  i 


6708 
6718 


5644566455 
56539665 


67191 


5Tv573 


6672766736 
5682066829 


67200 


67 24-7167256  67^6516727416728^  .    _ 
67339;6734s,67357j67367  67376,6  7385 
67410  67449  674596746867477 
67532  67541  67550 6755967569 
'  624  6-7633  67641 6765i'6766o 


69j  5  1 
68242 
4833- 
68422 
68511 
68601 
686-)r 
6878^ 
68869 
68057 


69196-69205  69214  69223 


692851692')  3169302 

69373;6938  <  (6939^ 
69460  66467169478 
6  5548  695  5-  •<"••*< 


69636  6964469653  69662 


69723!69732  69-74 


677i56772467733167742'67752 
67806  578i5  67324;678:;67S43 


7838|6/S97!67?o 


797 


80706807963038 
8i6oj6fT6r;'  B8T78 
8251 


256-7934 
680066801568024 
77|58io6  68115 

768T96 


8341 


6f?4.;o  6844 :; 


6852068529! 

586io  6R6IQJ63528 
6879868717 
6879768806 


88861688  ;s 


5.8278)68287 
58^6868377 
.5868467 


68 


&»547« 
686376864^ 


735 


68806688156882468833 


68  )O4.'6o9n 


^8_?75!l8_jiL:  6S9pji6_9oo2 


09055169064:690  / 3  69082169090  69099 
69143  6715216916  [|6';i7o:6->i79  69188 
69232  69241169 249!69253;6?267  69276 


68386 

68476 
68565 
58655 

68744 


6892 

69.-?;  i 


6932 


69509 

6948-7 

6957469583 


3716934^69355 


6940?  6941-7  69425  6943469443 
695*36951269531 


69749 


69810^981969827169836  _ 

"989  7  6990669914  69923  69932 
69984|699927000I  70010 
7007070079 70088  70096 


»03j7o  15-71 7oi65'7oi74  7oi8; 
}o47o2.'3'7o252 70260  -7026.: 


i°6  7o4 


5° 


I595'7o6o3 
•70672*70680  7068 


-70842-70851  -70859 


512-709 

•7101271020-71029 

5H 

515/71181  7n8/)7ii98 

7I2657I2737I282 


5i77i3497i3 


,    .      7^371 
7I45° 7145s 
7i5257I5337154 


OOi8 


7OI05  7OI147OI22|7OI3I  7013-. 
70191  7O2OO,7O2O97O2I7  7O226 


7°35" 
70441 

7°6l2 
70697 


7I03- 
7112 

71206 
7129^ 


750-4 
69592 
696-75 


5960169609 
69688169697 


;6l8 
59705 
*9793 

6j83c 

i;94.);699586o)66 
70027  70036700447005-: 


^9758  69766  6977516978 
"  ^45698 53  6986%  60871 


70277  70286,7029570303 
70363  7037217°38t70389 
7C44;7o458|7o466;7 


70535 

70621 


o7o6  70714  70 7 


70791 
7086870376 
7095270761 


705447055170561 


70800  77)8087 


7096; 


°73I 
0017 


7^873 70901 


710467105471 


7113871147  7115 

7*3°7|7!3I57I324 
7i39ii7I39vi7l4o" 
7147517^8-57140 


9364 
i9452 

59539 

>9027 
59714 
69801 
69888 

^9975 

70062 


704^4 

7056 


70-74- 


7031 

70398  70406 


7®  49  2 
70578 
•70663 
70748 

70834 
•70918 
•71003 
•71088 

-.71I7-.j 
7124871256 

7I33.27I34I  i 
71416)71425  || 
71500 7 1 508  & 
17x5847 1 50*'3 
m«Q» 


Logarithms  from   i  to  io,oco 


^**«7*i 

$&** 


Logar'thm  •  -rom  i  to  10,000 


^No. 

'580 

o 

1 

2 

3 

4    5    6 

7 

8 

<t  £} 

76343 

76350 

76358 

76365 

76373 

76380 

76388 

76395 

-6403176410  '. 

581 

76418 

76425 

76433 

76440 

76448 

76455 

76462 

76470 

76477 

6485 

582 

76492 

•^6500 

76507 

-6515 

76522 

7653° 

76537 

76545 

"6552 

6559 

583 

76567 

76574 

76582 

76589 

76597 

76604 

76612 

76619 

76626 

6634 

584 

76641 

76649 

76656 

76664 

76671 

76678 

76685 

76693 

76701 

6708 

767I6 

76723 

7673° 

76738 

76745 

76753 

76790 

76768 

76775 

6782 

586 

76790 

76797 

76805 

76812 

76819 

76827 

76834 

76842 

76849 

6856 

587 

76864 

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88497)88502  88508 


S877 
8882 


88615 
[8866698672 

87I7  8872288728 
Q Q_  Q  Q—  Q 

0077980784 
8883588840 

88891188897 
88947188953 
89003189009 
8905989064 
89115^9120 
80170189176 


8894 
88997 


8910. 


8927^ 


89387 

7  89443 
2  8949^ 

8955^ 

89601:, 


8982r 
89882 
89936 


8879o'88795!88Soi  888c 
888468885288857-8886 
88902  88908  88913  8891 
68958  8896/1""  ' 


89226189232 
8928289287 

8y33789343 
89393J89398 


3 

8  8945 
8050.;  89509 


8944 


38i73!88i7888i!. 
882301882358824 
882^788292882 
88343188   '"" 


38457i88463t8846 
8851.3  8«5i9p852 

88570885768858 
8862788632 


887348873988745 


887 


8901^ 


182 


890: 


89070  09076  89081 
891268913189137 

J  O  i  S  J  t 


s  * 

8903 
8908 
8914 


8983 


89293,8^9.8893048931 
89348:893548936018936 
°194o4(l8c  409)8941 518942 
9459:89465  8947o:8947 
95T5  89520  8952618953 
,,09504  89570,89575  8958118958 
89619  89625:89631,896368964 
89675  89680 .'896 861 8 g6o  118960 
89730  8273^18274.1  !£2746!£Q7  5 
89785  89790^9796  89801^980' 


9944 


^00266  90271 


9027619028290287 


90590 
90644 
90698 


10849 

,10902 

51OCC. 
.1062 


90907 
90961 


91121 


90428 
90482 


90596 
90650 

90703 
90757 


60855 

9091-5 


1286 
J339 


90380 


jooiS 


91025 
91078 
91132 

iii3* 

'1344, 


«yYO£»y/jpJoy7yi 

8984089845189851 

89894  89900j899°5 

89949|89955  8996^ 
^ooo4J9oco9  yOoi< 

900  ;• :; !90o64IOCfc'6'. 

90113  9011919012^ 
90168:9017310017" 

90^33 


89856:8986: 

899Il899i< 
899668997 
90020  9002 

9007  t;  9008 
901299013 


'°493;9°499 
90547  90553 

90601  90607 


90655  9066090666 


90709  9o7 


90504 


90612 


2072 


r-/~7|,7-/--r,.'  -  /  -~  - 

^0763190768  90773 

inftr  Xinr>fto-i  noR->i 


08169082 


10870  00875 


90827 

9o88"i 


^0024  90929  90934 

'°977|90982 

111030 

11084 


91036 


llf;o  91196 


018 


90184 

90238 


9056319056 
906179062^ 
90671 90677 


040 


90725 
90779 


91094  91100 
91148191153 
Q12OI 91206 
91254 


90730 
90784 
90838 
90891 

9094090941 

90993 


91265 
2i3l8 


^33< 

"0190 

88247 

88304 

88460 

384i- 

88474 

88530 

S85S' 

8864j 

88700 

887,6 

88812. 

38868 

88921; 

88981 

"9°3' 

9092 
'9148 

19204 

^9260 
:93J5 

9426 
948i 
9537 
9592 
9647 
9702 

97j>7 
9812 
9867 
9922 

9977 
0031 

0086 
0140 
0195 
0249 
0304 
0358 
0412 
0466 
0520 

°574 

628 

0682 

789 

843 
897 

95° 
004 
057 
no 
164 
217 


376 


Logarithms  from  i  to  10,000 


13 


^No. 
'820 
821 
822 

823 
824 
825 
826 
827 
828 
829 

t— 

o 
91381 

9*434 
91487 
9*54o 

9*593 
91645 
91698 

9*75* 
91803 

9*855 

i 

91440 
9*492 

9*545 
91598 
91651 

9*703 
9*756 
91808 
91861 

2 

2.1392 

9*445 
9*498 

91551 
91603 

9*656 
91709 
91761 
91814 
91866 

3 

4 

5 

6 

7 

8 

f  9  £ 

9*397 
9*45° 
9*503 
9*556 
91609 
91661 
9*7*4 
91766 
91819 
91871 

9*403 

9*455 
91508 

9*561 
91614 
91666 

9*7*9 
91772 
91824 

91876 

91408 
91461 
9*5*4 
9*566 
91619 
91672 
91724 

9*777 
91829 
91882 

9*4*3 
91466 

9*5*9 

9*572 
91624 

9*677 

9173° 

91782 

9*834 
91887 

91418 
91471 
9*524 
9*577 
9*630 
91682 

9*735 
91787 
91840 
91802 

91424 
9*477 
9*529 
9*582 

9*635 
91687 
91740 

9*793 
91845 
91897 

91429^ 
91482 
9*535 
9*587 
91640 
91693 

9*745 
91798 
91850 
91903 

830 
831 
832 

833 
834 
835 
836 

837 
838 

8^9 
840 
841 
842 

843 
844 
845 
846 

847 
848 

849 

91908191913 
9196091965 
9201292018 

9206592070 

92II7|92I22 
92169192174 

9222192226 
9227392278 
92324,92330 

91918 
91971 
92023 
92075 
92127 
92179 
92231 
92283 

92387 
92438 
92490 
92542 

92645 
92696 

92747 
92799 
92850 
92901 

91924 
91976 
92028 
92080 

92132 
02184 
92236 
92288 
92340 
92392 

91929 
91981 

92033 
92085 

92137 
92189 
92241 
92293 

92345 

02397 

9*934 
91986 

92091 

92143 
92195 

92247 
92298 
92350 

924.02 

9*939 
91991 

92.044 
92096 
92148 
92200 
9*252 
92304 

92355 
92407 

92459 
92511 
92562 
92614 
92665 
92716 
92768 
92819 
92870 
92921 

91944 
91997 
92049 
92101 

92153 
92205 

92257 
92309 
92361 

)24I2 

91950 
92002 
92054 
92106 
92158 
92210 
92262 
92314 
92366 
92418 

9*955 
92007 
92059 
921  n 
92163 
92215 
92267 

92371 
02423 

92474 
92526 
92578 
92629 
92681 
92732 
92783 
92834 
92886 
92937 

9242892433 
9248^92485 

9253I92536 
9258392588 
9263^92639 
926*6J9269I 
92737|92742 
92788192793 
92840  92845 
92891  92896 

92443 
92495 
92547 
92598 
92650 
92701 

9275'- 
92804 
92855 

92906 

02449 
92500 

^2655' 

)2-Jo6 

92800 

92860 

92911 

92454 
'.'2505 

92557 
92609 
02660 
92711 

92814 
9286=; 
?29£6 

92967 
93018 
93069 

93*20 

93222 
93273 
93323 
93374 
934-25 

93475 

93526 

93626 
93676 
93727 
93777 
93827 
93877 
03927 

02464 
92516 

92567 
92619 

92670 
92722 

92773 
92824 
Q2875 
92927 

92469 
92521 
92572 
92624 

;2675 

92727 
92778 
92829 
52881 
72932 

850 

851 
852 

853 
854 
855 
856 

857 
858 

859 

92942 

92993 
93°44 

93°95 
93*46 
93*97 
93247 
93298 
93349 
93399 

92947 
92998 
93049 
93100 

93202 
93252 
93303 
93354 
9J404 
93455 
93505 
93556 
93606 
93656 
93707 

93757 
93807 

93857 
93907 

92952 
93003 
93°54 
93*05 
93*  56 
93207 
93258 
93308 

93359 

93409 

92957 
93008 

93°59 
93110 

93*6i 
93212 
93263 
933*3 
93364 
93414 
93465 
935*5 
93566 
93616 
93666 
937*7 
93767 
93817 
93867 
939*7 

92962 

93OT3 
;3o64 

93**5 
93*66 

93217 
93268 

933*8 
93369 

93420 

92973 
93024 
93°75 
93*25 
93176 

93227 
93278 
93328 
93379 

93430 

92978 
93029 
93080 

93131 
93181 

93232 

93334 
93384 

93435 

9298392988 

9303493039 
93085193090 

93186193192 

9328893293 
93339'9  -44 
>>3389  93394 
93440  93445 

860 
861 
862 
863 
864 
865 
866 
867 
868 
869 

93450 
935°° 
9355* 
93601 

9365* 
93702 
93752 
93802 
93852 
93902 

9346o 

9356i 
93611 
93661 
937*2 
93762 
93812 
93862 
939*2 

93470 
93520 

9357* 
93621 
93671 
93722 
93772 
93822 
93872 
93922 

93480 

9353* 
9358i 
9363* 
93682 

93732 
93782 
93832 
93882 
93932 

93485 
93536 
93586 
93636 
93687 

93737 
93/87 

93S37 
93887 

93937 

;349° 
>354i 

9359* 
93641 
93692 
93742 
93792 
93842 

93892 

03042 

93495 
93546 
93596 
93646 
93697 
93747 
93797 
93847 
93897 
23947 
93997 
94047 
94096 
94146 
194196 
,94245 
,94295 
94345 
94394 

,94443e: 

870 
871 
872 

873 
874 

875 
876 

877 

3*79 

£f*> 

93952 
94002 
94052 
94101 

94151 
94201 
94250 
94300 
94349 
94399 

93957 
94007 
94057 
94106 
94156 
94206 
94255 
94305 
94354 
94404 

93962 
94012 
94062 
94111 
94.161 
94211 
94260 
943*° 
94359 
944°9 

93967 
94017 
94067 
94116 
94166 
94216 
94265 
943*5 
94364 
94414 

93972 
94022 
94072 
94121 

94171 
94221 
94270 
94320 

94369 
94419 

93977 
94027 
94077 
94126 
94176 
94226 
94275 
94325 
94374 
94424 

93982 
94032 
94082 

94131 
94181 
94231 
94280 
9433° 
94379 
94429 

94037 
94086 
94136 
94  1  36 
94236 
94285 
94335 
94384 
94*33 

93992 

94042 
94091 

94191 
94240 
94290 
9434C 
943  8<; 
94438 

J4 


Logarithms  from  i  to  10,000. 


"3  No. 

o 

i 

.2 

3 

4  f 

/>4473 
,'452;, 

?457i 
^4621 
24670 
94719 

94817 
94866 
94915 

6  i 

7  ) 

8  . 

9  '"^ 

94542  "'. 

9459i 

94640 

94787 
94836 
94885 

94983 
95032 
95080 
95129 

95177 
95226 

952/4 
95323 
95371 
95410 

95468" 
955i6 
95564 
95612 
95660 
95708 
95756 
95804 
95852 
95899 

881 
882 
881 
884 
885 
886 
887 
888 
889 
890 
891 
892 

893 
894 

895 
896 

897 
898 
899 

900 
901 
902 
,903 

9°4 
905 
906 
907 
908 

LOQ 
GIO 

9H 
9I2 

914 

915 
9l6 
917 
9l8 
019 

94448 

94547 
94596 

94645 
94694 

94743 
94792 
94841 
94890 

94453 

94502 

94552 
94601 
^•650 
94699 
94.748 
94797 
94846 
94895 
94944 

94993 
95041 
95090 

95139 
95187 

95236 
95284 
95332 

,44.,- 
745°  7 
94557 
94606 
94655 
94704 

94753 
94802 

74851 
9490° 
94949 
94998 
95046 
95°95 
95143 
95192 
95240 
95289 
95337 

9446394468 

,14562  94567' 
946  1  1  19461  6| 
/466oj94-665j 
94709,9,  714 

948o7J948i2 
9485694861 
94905194910 

H527 
^4626 

H7-4 

5>4?22 

^4871 

24919 

94968 

95017 
25066 

95114 
95163 
95211 
95260 

95308 

95357 
95_4o'5 
95453 

95550 
95598 
95646 
95694 
95742 
95789 

95837 
95885 

94483 
94532 

94630 
94680 
94729 
94778 
94^27 
94876 
94924 

94973 

9502.2 

95071 

95119 
95168 

95216 
95265 
95313 

954io 

94488 

94537 
94586 

94685 

94734 
94783 

94880 
94929 
94978 

95027 

95075 
95124 

95173 
95221 
95270 

95366 

95415 

94939 
94988 
95036 
95085 
95134 
95182 

95231 
95279 

-5328 
95376 

94954 
95002 

95051 
95ico 
95148 
95197 

95245 
95294 
95342 
25399 

94959 

05007 

;5056 
95105 
95*53 

95202 

95250 
95299 
95347 

95305 

94963 

95061 
95109 
95158 

95207 

95255 
95303 

95^52 

95400 

95424 
95472 
'5521 
95569 

95665 

57*3 
95761 
95809 
95856 
95904 
95952 

95999 
96047 
96095 
96142 
96190 
96237 
96284 

95477 

95434 
95482 

95439 
95487 
95535 

95651 

9567v 

95727 
95775 

95871 

y5444 

95540 
95588 
95636 
95684 
95732 
95780 
95828 
95875 

95448 
95497 
95545 
95593 
95641 
95689 
95737 
95785 
95832 
95880 
95928 
95976 

,0023 
96071 
96118 
96166 
96213 
96261 
96308 
96355 

95458 

25554 

95602 
95650 
25698 
95746 
95794 
95842 
95890 

95463 
95511 

95559 
95607 

95655 
9"5  7°  3 

95751 
95799 
95847 
95895 

95574 
95622 
95670 

95766 

95861 

959°9 
95957 
96004 
96052 
96099 
96147 
96194 
96242 
96289 
96336 

9553° 
95578 
95626 

9577° 
95818 
95866 

959** 
95961 
96009 
96057 
96104 
96152 
96199 
96246- 
96294 
96341 

95918 
05966 
96014 
96061 
96109 
96156 
96204 
96251 
96296 
96346 

9639: 
96440 

96487 

9653^ 
96581 
96628 

96675 
96722 
96769 
96816 

95923 

^6019 
96066 
96114 
96161 
96200 
96256 
96303 

95933 
95980 
96028 
96076 
96123 

96171 
96218 
96265 
9631- 
96360 

95938 
95985 

96033 
96080 
96128 

96i75 
96223 
(96270 
96317 
96365 

95942 
95990 
96038 
96085 

9613: 
96180 
96227 
96275 

963? 

6369 

95947 
95995 

96042 
96090 

96137 
96185 
96232 
96280 
96327 
96_374 
96421 
96468 
96515 
96562 
96609 
96656 
96703 
96750 

96797 
96844 

96890 

96937 
96984 
97030 
97077 
97123 
97169 
97216 
97262^ 
97303C 

920 
921 
922 
923 
92^ 

926 
92- 

92 

21 
93C 
931 
932 

933 
9^^ 

935 
93^ 

1937 

li 

90379 

96426 

96473 
96520 

96567 
96614 
9666 
96708 

96755 
96802 

96384 
96431 
96478 
96525 
96572 
96619 
96666 

96713 
^6755 
96806 

90388 

96435 
96483 

9653C 

96577 
96624 
96670 
96717 
9676^ 
96811 

96398 

96445 
96492 

9653', 
96586 

9663: 
96680 

96727 
96774 

96820 

96402 
96450 

96497 

96591 

96685 

96731 
96778 
9682.' 

96407 
96454 
96501 
96548 

96595 

96642 
96689 
96736 
96783 
96830 

96412 

96459 
96506 

96553 
9.'6oc 

96694 
96741 
96788 
96834 

96417 
96464 

96511 
96558 
96605 

<,6«5a 

96699 

96745 
196792 
196839 

96848 
96895 
96942 
96988 

97035 
9708 

07128 
97174 
97220 
9726- 

96853 
96900 
96946 
96993 
97035 
97086 

97179 

97225 
97171 

9685S 

96904 
96951 

96997 
97044 
97090 

97*37 
97183 

9723C 
97276 

96862 

96956 
97002 
97049 
97095 
97142 
97188 
97234 
97280 

96865 

9691, 
96960 

9705- 
97100 
97146 
97192 

97239 
97285 

96872 
96918 

96965 
97011 

97104 

97151 
97197 

97243 

197290 

96876 
96923 
96970 
97016 

97109 

97*55 

97202 
9724 
97294 

96881 
96928 
96974 

97021 

97067 
97114 
97160 

97206 

97253 
97299 

96886 
96932 
96979 
97025 
97072 
97118 

97165 
97211 

97257 
197354 

i:eS^ 


rrithms  from  i  to  10,000 


944 


962 
963 


979 
980 
981 

982 

98 
98 

985 
98 


73I3!973.I7973a.2 


735997364 
7405197410 
7451197456 
749797502 
7543197548 
7589J97594 
7635:9764- 
7681,97685 

7727J9773/ 

7772'97777,,,-- 
78189782397827 
7  864  97  868 
79°9979I4 


804698050 
8091 98096 
'813-798141 
1818298186 


97327 


J  i   «J 

97877 

-,  ™  . ,  -  ... ,  97923 
795597959979C497968 
800098005  •-' ° 


91 


98009 


.97373 
9741497419 
9-7460  9-7465 
9750697511 

97557 

9759897603 

07644 

9-7690 


9774C 


9778297786 


9801. 


l8227|98232 

>8272j98277 
(831898322 


9s°53j/°5$ 
'810098105 
'814698150        „ 
18191  98^95  98200 


8363 

-040* 
8453 
8498 


8677 
8722 
98767 
98811 
9885 
98900 

98945 
98989 


99167 
9921 


99344 


99476 


9(2607 


8367 

8412 


8547 
98592 
8637 


98682 
98726 

98731 

98816 
98860 
98905 

98949 

,18994 

99038 

99083 

99127 

991-71 

99211 

9926- 

99304 

99348 

99392 

9943^ 

9948' 

9952- 

99568 

99612 

9965 
9960 

997399974 
99782  99-78 
998269983 

7870  99874 
999 i 3 999 l 


99957 


. 

0096  1 


,97336" 
737797382 


97653 
97699 
97745 


97836 
97882 
97928 

97973 
98019 
98064 
98109 


8236 
8281 

8327 
8372 


98507 
98552 
y8597 
(8641 

;~8~68l 

9873! 


9833 
98376 


9886 


,   .  98245 
982869829 


9833* 

9838 

98426 


984669847, 
9851119851* 
985569856 


9860 
98646 


98691 

98735 
98780 


9882098825 


98869 


98909198914 


,-98700 

9874o  ,  . 
987849378 
988299883 
9887498878 


98954 


99043 
99087 


99092 


99I3I 


99136 


99352 


99484 


9961^ 


yyy^S 


8958 


98918 


98998  99003 
9904-5 


991769918 

99220  0922  , 
99264  99269 
9930899313 

99357 
9940 1 

9944f 
99489 
99533 


99577 


997°fc 


7612 


2149 
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•       ,  )cgr 

Artificial  Sines,  TangJ.  and  3eu.4/;<i)'egrees 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
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